He was still completing the quarantine process having travelled to Dubai with his family, separate to the contingent of Royals players who had come on a private charter direct from the England-Australia series in the UK.
Sanju Samson hit a blistering 74, and captain Steve Smith also hit a half-century having opened the innings.
Buttler is likely to be restored to the top of the order when the side play Kings XI Punjab in Sharjah on Sunday.
He says he was delighted by what he saw in the opening game while watching back at the team hotel in Dubai.
“It was great to get a win on the board, the team played fantastically well in the first game,” Buttler said. “It was an outstanding batting performance and a fantastic bowling performance in tough bowling conditions.
“I am really excited to play my first game. It was great to be back in training with the boys, there’s a great vibe around the team so I'm really looking forward to taking the field.
Rajasthan v Chennai player ratings
“The atmosphere and energy around the squad is fantastic, obviously lots of confidence after that first game.
“The training has been very energetic, guys are lively and enjoying each other’s company.”
Buttler also appreciated the performance of another wicketkeeper-opener, KL Rahul, who made a hundred against Royal Challengers Bangalore on Thursday.
It was the highest score by an Indian in IPL history, and Buttler said his side will have to be at their best to halt him this time around.
“We are expecting a really tough match against Kings XI,” Buttler said.
“They are a fantastic team, and KL Rahul was in exceptional form the other night against RCB. He will be a key wicket as always.
“I think we’ll see another potentially high-scoring game at Sharjah with small boundaries and the dew factor coming in. Can’t wait to get back out there.”