The striker, who joined Liverpool from Chelsea earlier this week, scored the opening goal of Liverpool's 2-1 success at Mansfield.
Sturridge admits he enjoyed his first outing with his new club and felt he could have scored more than one goal after an impressive debut.
"I enjoyed it very much. It was my first game for the team, and it was great to get to know my teammates on the field and to win the game," Sturridge told ESPN.
"It was a great ball from Shelvey and I got on the end of it and put it away.
"I am disappointed [I didn't get more goals] but the team played fantastically and showed a lot of character, and I'm delighted with the win."