Pirlo was named as Sarri's successor last month and marked his first competitive game in charge with an impressive 3-0 win over Sampdoria last weekend.
Ramsey, who was in and out of the side last season, enjoyed arguably his best game for Juve as he created an unrivalled six chances – including an assist for Cristiano Ronaldo.
And the Wales international revealed the mood has now changed in the dressing room on the back of iconic former midfielder Pirlo's appointment.
"We have a new coach, a new staff, new ideas and the players are very involved in this," he told Sky Sport Italia.
"I think we are having more fun than last year. The training sessions are hard but there is also a little bit of joy."
Dejan Kulusevski and Leonardo Bonucci were also on target for Juventus in their opening match, but Ramsey believes there is still more to come from his side ahead of Sunday's trip to Roma.
"We started well but we still need to improve," he said. "In this team there are many great players, who can all play and help the team reach their goals.
"I'm happy to be able to play together with these top-quality attackers."
Inter finished just a point behind Juve last season and are expected to push the champions all the way this campaign after spending big during the close season.
Ramsey is predicting a tight battle at the top this term, adding: "Inter are a great team and have signed a lot of players. They are are one of the contenders for the Scudetto.
"Like Napoli, who are very strong. Milan finished last season well and started the same way. Serie A is a very tough league."
The Wales international has struggled for appearances this season and was told by Juve boss Massimiliano Allegri to find a new club this month.
Ramsey had been linked with a number of Premier League sides, including Wolves, Burnley and Crystal Palace, but he sealed a deadline-day switch to Rangers on Monday.
He will spend the rest of the 2021-22 campaign at Ibrox, with an agreement also reportedly in place for Rangers to sign the midfielder permanently at the end of the season.
"I am really pleased to be joining a club like Rangers, where there is so much to look forward to between now and May," Ramsey told Rangers' official website.
"I had a number of offers on the table, but none matched the magnitude of this club, with European football and the chance to play in front of 50,000 fans every other week.
"I have had some fantastic conversations with the manager and Ross Wilson, and I'm really looking forward to working with both of them, and to meeting the supporters."
Rangers boss Giovanni van Bronckhorst added: "I'm absolutely delighted that we have been able to add a player of Aaron's quality, experience and leadership to our squad.
"As soon as it was mooted as a possibility, I was really keen for us to try everything to get the deal done, and huge credit must go to Ross and to the board for the work they have put in on this.
"I look forward to welcoming Aaron to the training centre tomorrow."
Ramsey will be looking to kick-start his career back in Britain with Rangers following a largely frustrating time of things across his two and a half years with Juventus.
The 31-year-old, who previously spent 11 seasons with Arsenal, has struggled for regular appearances at the Allianz Stadium due to persistent injury problems.
He has started just 34 games in all competitions since making his debut in September 2019, with 16 other players featuring more regularly for Juve over that period.
While his playing time has been limited, Ramsey's 2.07 chances created per 90 minutes during his time in Turin is the best return of any midfielder currently in the squad.
Since Allegri's arrival at the start of the season, Ramsey has been used only five times – and not at all since early November – totalling 111 minutes of action on the field.
The Cardiff City academy product is eligible to make his Rangers debut in Wednesday's Old Firm showdown with Celtic.
The Gers announced the signing of Mateusz Zukowski from Lechia Gdansk earlier on Monday.
Former Real Madrid forward Bale retired from professional football at the age of 33 in January, having led Wales into their first World Cup campaign since 1958 in Qatar last year.
Having won a record-breaking 111 caps for his country, Bale will be succeeded by the man joint-seventh in their all-time appearance list – former Arsenal and Juventus midfielder Ramsey.
Ramsey moved to France in search of regular minutes following a frustrating loan spell at Rangers last term, and has made 21 league appearances since joining Nice on a free transfer last August.
The 32-year-old already has experience of captaining Wales after being named skipper by Gary Speed in 2011, though Chris Coleman opted to hand the armband to Ashley Williams one year later.
The announcement came as boss Rob Page named a 24-man squad for Wales' opening Euro 2024 qualifiers against Croatia and Latvia later this month, with the team looking to qualify for a third-consecutive edition of the tournament.
Page named four uncapped players in his squad for those fixtures, namely midfielders Jordan James and Ollie Cooper, Fulham youngster Luke Harris and striker Nathan Broadhead.
Wales finished second in Group E to earn home advantage in March's play-offs after they fought back from a goal down to draw 1-1 with Belgium on Tuesday.
Kevin De Bruyne had put Belgium ahead early in the game before Moore equalised just after the half hour.
Moore's goal was his eighth for Wales since making his international debut in September 2019 – more than any other Wales player in that time.
"It's so important to get a home draw," Moore told Sky Sports.
"If you look at the teams that have come in second, the likes of Portugal and Italy - it's been a bit nervy. But nights like this, I'd back us to take on anyone.
"We left everything out there. We gave everything for that performance because we knew we needed a result.
"The noise after that goal, it was just incredible. I can't explain it, I was lost for words. It's some feeling, I'll say that. The Red Wall [Wales fans] are amazing.
"We knew that Belgium would try and keep as much possession as much as possible so we knew we had to be compact, be tight and not let them through us so that we could get them on the counter-attack."
Wales have lost just two of their last 20 World Cup qualifying matches (won nine, drawn nine) and are unbeaten in their last seven heading into the play-offs next March.
They have also finished in the top two of a World Cup qualifying group for the first time since qualification for the 1966 World Cup, when they finished second (only the first-placed teams qualified that year).
Wales captain Ramsey hailed the willingness of his team-mates put their heads where it hurts against Belgium to clinch a play-off spot.
He added: "Full credit to the boys, they put in a massive shift again against top opposition.
"We always believed we could get a result, especially with our fans behind us. It's another good night for us.
"We build our foundations on everybody putting in a shift for each other, putting their bodies on the line, and we managed to do that again tonight.
"There's some big, big teams still in it but it was so important that we had a home tie. You could see the atmosphere tonight – it's a special place to come and play. Hopefully that will give us an extra edge in that first play-off."
Wales boss Robert Page acknowledged his side suffered from the absence of the injured Gareth Bale against Belgium, with hopes of reaching first World Cup since 1958 now tantalising within reach.
He said: "We're always going to miss Gareth but there's so much he brings to this team off the pitch too, just having him around the dressing room. He wanted to be with us tonight, he's a proper captain.
"When the crowd is behind us like it was tonight, we'll take on anyone. We're not done yet; we're dreaming of a World Cup but it's definitely achievable."
