Clijsters remains winless since coming out of retirement on the WTA Tour, falling 6-1 2-6 6-2 to Katerina Siniakova on Thursday.
A four-time grand slam champion, the 38-year-old Clijsters has lost all five of her singles matches since her return last year.
"I think overall, there's definitely moments where I'm feeling really good out there, and there's moments where I feel too inconsistent," Clijsters – a winner at Indian Wells in 2003 and 2005 – told reporters.
"That's part of this process in general, it's not going to be a smooth ride, and that's what I'm going to try to improve every time I'm out there."
World number 53 Siniakova converted six of nine break points on Clijsters' serve and moved on to face 10th seed Angelique Kerber at the WTA Premier 1000 event.
GOLUBIC HOLDS OFF VONDROUSOVA
The day's only duel between top-50 players saw world number 46 Viktorija Golubic outlast 37th-ranked Marketa Vondrousova 6-1 4-6 6-3.
Both players struggled with their own service games, combining for three aces and 17 double faults, but it was the Swiss who managed to convert on eight of 14 break-point chances and come out on top.
It was Golubic's first win against a player in the top 50 since joining those ranks herself in July; she had been 0-3 against them since then.
GARCIA RALLIES PAST FLIPKENS, RISKE GETS RARE INDIAN WELLS WIN
Caroline Garcia fought back to defeat Kirsten Flipkens 5-7 6-4 6-0 in a match that took two hours, nine minutes to complete, firing seven aces and winning 71.2 per cent of points on her first serve.
The Frenchwoman, who had been upset by qualifiers at her two previous tournaments in Ostrava and Chicago, meets 15th seed Coco Gauff in the second round.
Alison Riske celebrated a victory for just the second time in seven trips to Indian Wells, cruising past qualifier Liang En-shuo 6-2 6-2 to set up a second-round matchup against 16th seed and former US Open champion Bianca Andreescu.
Organisers confirmed on Sunday that the WTA event and the ATP Indian Wells Masters, which were both scheduled to start on Monday, had been called off due to concerns over the coronavirus.
The Riverside County Public Health Department declared a public health emergency on Sunday after a confirmed case in Coachella Valley.
World number 77 Flipkens reacted with angry surprise to a tweet from the official tournament account that confirmed it had been called off, saying: "And the players had to find out... through Twitter...".
When American player Nicole Gibbs replied to tell Flipkens "There was an email", the Belgian responded: "I saw it on Twitter first."
She also sent a message to the WTA and urged fellow professionals to share it, saying: "@WTA isn't the least you can do is [sic] organising an emergency meeting with the players????"
Rising American star Coco Gauff said she was "so sad" that the event had been cancelled. The 15-year-old had been due to make her debut at the event this week.
"Safety is always the no.1 priority," she tweeted.
Meanwhile, Jamie Murray expressed concern over the rest of the 2020 calendar given the Indian Wells tournaments were called off due to just one confirmed coronavirus case.
"Doesn't bode well for the tour if IW cancelled for 1 confirmed case in Coachella Valley," he wrote on Twitter. "Broward county (Miami Open home) has more confirmed cases. Monte Carlo borders northern Italy currently in lockdown. Rome Masters? French Open? Wimbledon?!!!"
In a statement following the Indian Wells cancellations, WTA chairman and CEO Steve Simon said: "It is too soon to speculate about what will happen to other tournaments that follow.
"We will continue to closely monitor the situation. Health and safety will always come first."
Hurkacz made it through a tough encounter against Stan Wawrinka 7-6 (7-5) 6-4 to give Poland a 2-1 lead in their Group B tie with Switzerland in Brisbane, before Linette came from behind to beat Jil Teichmann 5-7 6-4 6-1 to clinch it.
Poland will face Italy in the Brisbane final, whose 5-0 whitewash of Norway included Matteo Berrettini sealing victory with a 6-4 6-4 win over Casper Ruud.
In Perth, Croatia advanced to the City Finals after a dramatic day that saw Caroline Garcia get France on the board with a straight sets win against Petra Martic, before Adrian Mannarino came from a set down against Borna Gojo to serve for the match as he looked to bring his country level at 2-2.
However, Gojo broke back in a tense encounter before winning a deciding tie-break to send Croatia through to face Greece, who sealed a 4-1 win against Belgium.
Stefanos Sakellaridis recovered from going a set behind to beat Zizou Bergs, before Maria Sakkari overcame Elise Mertens 6-1 7-5, with Sakkari and Stefanos Tsitsipas adding some gloss to the score with a mixed doubles success against Kirsten Flipkens and Michael Geerts.
Spain and Australia were unable to progress but the hosts at least had the consolation of securing a victory thanks to wins for Jason Kubler against Albert Ramos-Vinolas, and the mixed doubles duo of John Peers and Sam Stosur against Jessica Bouzas Maneiro and David Vega Hernandez.
The USA had already secured their Finals berth against Great Britain in Sydney, but were ruthless as they finished off their tie against Germany to win 5-0.
After Jessica Pegula beat Laura Siegemund 6-3 6-2, Frances Tiafoe also defeated Oscar Otte in straight sets, before the American duo combined to beat Siegemund and Daniel Altmaier 6-7 (5-7) 6-4 10-7 to complete a clean sweep.
With a month to go before Kenin begins the defence of her Australian Open title, the American world number four was fighting to avoid a second-round exit to an experienced opponent.
Flipkens took the first set 7-5 and trailed 5-4 in the second, a break down, when an injury to her left ankle caused her to retire from the match.
A run of three consecutive games and 12 unanswered points from Flipkens had seen the 34-year-old former Wimbledon semi-finalist snatch the opener.
Kenin was turning the contest around in the second set and the top seed admitted she was "a little bit upset" to see Flipkens suffer when injury struck.
"We're good friends and that's not something you like to see," Kenin said, quoted on the WTA website. "I just hope [Flipkens] can have a speedy recovery and get ready for Australia.
"She played a really good match. It was the third time we’ve played each other, and it was a really solid match from both of us. This is not the way I wanted to win."
Aryna Sabalenka could be a player to fear at Melbourne Park in February, as the world number 10 made it 11 consecutive match wins by fending off Australian Ajla Tomljanovic 7-5 6-4.
Sabalenka finished off the 2020 season with titles in Ostrava and Linz so the Belarusian is looking for a hat-trick of tournament triumphs.
Tunisian Ons Jabeur scored a 5-7 6-3 6-2 victory against Kateryna Bondarenko of Ukraine to reach the last-16 stage, and she faces Sabalenka next.
Jabeur won on the only previous occasion she and Sabalenka have met, securing a three-set win in round three of the delayed 2020 French Open.
Kudermetova had won her only two previous singles matches against Kontaveit and maintained that perfect record with a 7-5 6-1 victory.
The world number 46 from Russia broke four times to seal her place in the second round, with Kontaveit winning just 48.4 per cent of points on her first serve in a rusty beginning to the 2021 campaign.
Donna Vekic was another seed to fall at the first hurdle as Bernarda Pera consigned the Croatian to a 7-6 (12-10) 2-6 6-4 defeat at Zayed Sports City International Tennis Centre.
Kirsten Flipkens could face top seed Sofia Kenin in the second round after defeating Laura Siegemund 5-7 7-5 6-4.
Ons Jabeur is aiming to break into the top 10 this year and the 15th seed got up and running for the season by seeing off Anastasia Pavlyuchenkova 7-6 (7-3) 6-3.
Daria Kasatkina, Yulia Putintseva and Ajla Tomljanovic were among the other players who advanced to round two.
