The winger saw his lucrative move to Manchester City in 2012 fail to bring him the experiences he craves in Europe’s elite club competition.
Sinclair made just one appearance for City in the Champions League, playing 57 minutes in a meaningless 1-0 defeat away to Borussia Dortmund.
The 27-year-old is now reunited with his mentor Brendan Rodgers, having completed a £3.5 million switch from Aston Villa to the Scottish champions at the weekend.
Fresh from scoring the winner in Sunday’s 2-1 defeat of Hearts at Tynecastle on his debut as a second half substitute, Sinclair’s thoughts have already turned to Celtic’s Champions League play-off tie against Hapoel Beer-Sheva of Israel later this month.
“It would be massive for me to get into the Champions League,” he said. “It would be great for the club and the fans to get into the group stage.
“We have two more games to get through, so it is up to us to win that tie and make sure we get there.
“When I made my one appearance for City in the Champions League, there wasn’t anything on the line because the group had already been decided. It wasn’t a game we needed to win or anything like that. So it would be a massive deal for me to get there with Celtic.
“I definitely believe I will have the best years of my career here. Once I am settled, happy and stable in playing football again, then that’s when hopefully the Celtic fans will see the best of me.
“I couldn’t have asked for a better start at all on Sunday. I didn’t think I was going to be involved in the squad.
“I literally had three hours sleep on the Friday.
“My agent rang me late at night and said I had to get up to Glasgow quickly. I had to pack all my stuff.
“It was a bit of a rush but then the manager asked me if I was fit to play and be part of the squad. I didn’t look back from there.
“Brendan has been a massive influence on my career, having worked with me for so long. He got the best football out of me at Swansea and that got me a move to Manchester City,” added Sinclair.
“Now in my career I want to get that emotion back – the excitement of playing football.
“As a player it’s hard when you are not playing regularly so it’s about being strong and driving to get another breakthrough.
“I’ve got that breakthrough now signing for Celtic and I want to kick on.”