The 33-year-old skipper was utilised as a second-half substitute in a game where Cyriel Dessers cancelled out Ayoub El Kaabi's opener at the Karaiskakis Stadium on Thursday.
It was a call that raised a few eyebrows given the criticism Tavernier has faced this season, but Clement said it was just about managing the experienced full-back's minutes.
In quotes reported by BBC Sport, Clement said: "That's never an easy decision, but I want more than one captain in the group.
"If you come at a certain age you can't play 60 games at the same level. We knew that before the season. It's about competition for spots.
"It's about one team, winning together. That's Rangers - one team, one family, going for one goal."
Rangers now have seven points from four games in Europe's secondary competition, sitting just outside the top eight in the table.
Clement, however, was disappointed not to travel home with the win despite being impressed with the performance.
"A very strong performance as a team, sticking to the plan, being very disciplined and using the spaces," he added.
"Disappointed we didn't win the game, that's the next step we need to take. But I saw a lot of positive things and I need to praise the whole team for that.
"I don't want players happy with a point. We went for the three points and that's the mentality I want to see against any opponent.
"Our midfield was massive today. Our defence was really solid. Jack [Butland] didn't have to make many saves."
Rangers are now unbeaten in their last five away matches in the Europa League (W2 D3), equalling their longest such run in the competition’s history (also five unbeaten between October 2020 – March 2021).
Up next in the competition is Ligue 1 side Nice, who drew 2-2 with Enschede on Thursday.
Marinakis tested positive for coronavirus on March 10 and was treated back in his homeland.
The 52-year-old announced two weeks later that he had fully recovered from the virus and praised the "hero" health workers who treated him.
Marinakis has now contributed money towards an ICU at the General Public Hospital of Nikaia.
In a statement, Olympiacos said Marinakis had provided "once more a helping hand so that our public health system may cope with the huge challenges that have occurred".
They said: "The leader of Olympiacos along with Mrs. Aggeliki Fragkou and ΙΟΝ SA ΙΟΝ Α.Ε. donated an amount that exceeded €1.5m in total to be used for the procurement of 12 fully-equipped ICUs spaces (ICU-specific beds, high-tech ventilators, specific monitors, pumps, defibrillators, etc..), payment of all required installation and room configuration costs, E/M works, health and medical equipment, as well as all additional costs of the additional extension of the Hospital's intensive care unit."
It is hoped the new facility will be ready to receive patients in the next two months.
Greece has recorded 2,011 confirmed cases of coronavirus and 90 deaths.
Marinakis, who also owns Championship club Nottingham Forest, confirmed on Instagram that he had been diagnosed with coronavirus after showing symptoms of the illness upon returning to Greece on Monday.
Following that news, Olympiacos' players, board and staff members were all tested for COVID-19 and the club have confirmed that no one else has the virus.
"Olympiacos FC informs that after the required medical exams to which all the members of the football staff, as well as board members and staff, were submitted, all the tests came out negative for the COVID-19 virus," the club said in a statement on Wednesday morning.
Olympiacos host Wolves in the first leg of their Europa League last-16 tie on Thursday and the game is set to go ahead behind closed doors despite the Premier League side's protestations.
Wolves asked for UEFA to postpone the fixture in light of Marinakis' positive test, stating that "the trip poses unnecessary risk to our players, staff, supporters and the families of all who travel", yet European football's governing body rejected the request.
Olympiacos had progressed to the last 16 by beating Arsenal on away goals thanks to a 2-1 success in London on February 27.
Marinakis was at that fixture and had "come into contact" with personnel from the Gunners, which has led to Arsenal's Premier League fixture against Manchester City, scheduled for Wednesday, being postponed as a precaution.
Arsenal's players are self-isolating at home while four staff members will also remain at home until the two weeks are complete - dating back to the last time they had contact 13 days ago.
The two matches on Thursday are the latest to be impacted by the coronavirus crisis.
The Greek government enforced a temporary suspension of spectators attending sporting events on Sunday, with 73 confirmed cases of the virus in the country as of Monday.
UEFA subsequently affirmed the decision would affect Olympiacos in European competition, and Wolves will refund travelling fans who bought tickets.
Meanwhile, Roma's trip to Sevilla likewise will not allow supporters, following the example of Valencia v Atalanta – a Champions League encounter between Spanish and Italian teams.
The fixture will go ahead in Spain, where there are 999 cases and 16 deaths, although sporting events in Italy have been halted until April 3.
Italy is the European country most heavily affected by the virus, with 7,375 cases and 366 deaths.
A number of Serie A fixtures had been postponed even before Monday's decision to implement a four-week stoppage.
The opening leg will take place behind closed doors in line with Greek government policy aimed at containing the spread of coronavirus.
Earlier on Tuesday, Olympiacos owner Evangelos Marinakis announced he had tested positive for COVID-19 in Greece, placing the fixture in doubt.
Wolves issued a statement to express disappointment over the decision to proceed with the match.
The statement read: "Our position is that the trip poses unnecessary risks to our players, staff, supporters and the families of all who travel, at such critical and uncertain times.
"Our concern is also for our opponents, whose players and staff have today been tested, and will now be expected to play their part in an important fixture, under the difficult and challenging circumstances of their owner suffering with the virus.
"There is also disappointment that the match will be played without home and away supporters, as that is part of what makes European competition so special, as well as the fact our fans have already contended with similar obstacles on our Europa League journey already this season.
"We believe that there are some things that are more important than football, and that the good health of our pack and the general public is one of them. However, we respect the decision of UEFA and the integrity of the competition, and we will travel tomorrow to Greece to play the fixture.
"We hope that our request to UEFA, and our acceptance of their decision, can act as the catalyst for them to consider alternative options moving forwards, as this will not be the last fixture to be affected by coronavirus."
Earlier this month, Wolves sought to take a pro-active measure against coronavirus by banning players from taking selfies with fans.
The result left Rangers just outside the top eight in the Europa League table, while Olympiacos are one place further back, having picked up seven points from their four games.
Dessers, however, squandered a golden opportunity in the 11th minute after being sent through on goal, but could only fire his effort at the legs of Konstantinos Tzolakis.
Tzolakis was again on hand to deny the Rangers striker six minutes later, producing a stunning save to tip his effort wide as the Scottish side ended the half in the ascendency.
But their good work was undone shortly after the restart when Chiquinho's smart backwards header found Ayoub El Kaabi, who swivelled and rifled the ball into the roof of the net.
However, Rangers responded eight minutes later, with Dessers finally getting the better of Tzolakis. The Nigerian skipped beyond the challenge of Panagiotis Retsos before curling the ball home.
Both sides pushed to try and find the winning goal in the closing stages, but the spoils were shared at the Stadio Georgios Karaiskaki.
Data Debrief: Oh I do love playing away
Rangers can leave Greece happy with a point, though could have returned to Ibrox with all three after a strong showing against Olympiacos.
They ended the contest with an expected goals (xG) total of 1.13 compared to their opponents' 0.68, despite having three less shots throughout the contest.
But their impressive form away from home in Europe continued. They are now unbeaten in their last five away matches in the Europa League (W2 D3), equalling their longest such run in the competition’s history (also five unbeaten between October 2020 – March 2021).
Dessers also impressed for Philippe Clement's side. He has been directly involved in 10 goals across 13 away appearances in major European competitions (eight goals, two assists).
The former Monaco, Real Madrid and Everton midfielder moved to Greece at the beginning of the season, but departs having not played for the club since mid-February due to injury.
A statement from Olympiacos read:" James will always be part of our club and a member of the 'red and white' family. We want to thank him for his service and we wish him every success in the future."
In his own message on social media, James said: "I would like to thank everyone for all the time that we have spent together.
"Although we are going our separate ways, I feel that I will always be a member and welcomed in the family of the great port Piraeus. I wish all the best to Olympiacos and every success in the future."
A breakout star from the 2014 World Cup in Brazil, James is now on the hunt for a new club having struggled to find stability in recent years.
James has not spent more than a single season at any of his last three clubs – Olympiacos, Al-Rayyan and Everton – while a two-year loan stint with Bayern Munich from 2017-2019 saw the Bundesliga giants decline to make a permanent move.
He remains a regular at international level with Colombia, however, scoring in a 2-2 draw with South Korea last month and boasting 90 caps for his country.
The Belgian striker revealed his regret at leaving Inter for Chelsea in August.
Lukaku was subsequently dropped by coach Thomas Tuchel for Sunday's 2-2 draw with Liverpool.
TOP STORY – LUKAKU COULD MAKE STUNNING SWITCH TO SPURS
La Gazzetta Dello Sport claims that unsettled Chelsea forward Romelu Lukaku could make a cross-city switch to Tottenham to re-unite with Antonio Conte.
Lukaku and Conte worked together at Inter where they won the Serie A title last term.
The striker revealed his frustrations at Chelsea over the weekend, with Tuchel offering no guarantees about his future.
ROUND-UP
- Erling Haaland will not leave Borussia Dortmund during the January transfer window, reports Fabrizio Romano. Haaland has not decided his next destination yet, despite rumours of a pre-agreement with Real Madrid and Barcelona.
- Ara claims Barcelona will offer Ousmane Dembele to Manchester United as part of a swap deal for want-away forward Anthony Martial.
- Tottenham and West Ham United are both keen to sign Wolves' Adama Traore, claims the Telegraph. Wolves want £20million for the Spanish forward.
- Olympiakos' Guinea international midfielder Aguibou Camara is attracting interest from Milan and Liverpool, claims Calciomercato.
