Sturridge started the game against MSK Zilina, as the Blues rested Didier Drogba.
Chelsea won the gam 4-1 in Slovakia and Sturridge scored The Blues’ fourth goal.
“I’ve been dreaming of this since I was a young boy,” Sturridge told Sky Sports.
“I’m delighted to get off the mark in the Champions League and hopefully there’s many more to come.
“There’s a lot of world-class players in this team. I’m delighted to be part of things.”
“We played some good football in the first half hour,” Sturridge added.
“We wanted to play the ball quickly and try to make sharp movements in the attacking half of the field and to defend well, and I think we did that quite well and it paid off for us in the end.
“Zilina were playing at home so they had the fans behind them and were attacking a lot but I think the defence played pretty well tonight. We were unlucky to concede a goal but we’re going to come back stronger in the next game.
“We came out here to win and we’re delighted to do that. I think everyone will be happy with the win because the main thing was to do that in the Champions League. To get three points on the board is fantastic for the team.”
