Sturridge joined the Reds from Chelsea for £12 million earlier this month, and became the first Liverpool player since Ray Kennedy in 1974 to score in each of his first three games for the club, as Rodgers' side claimed an emphatic 5-0 victory over Norwich City.
The England international revealed his joy at being given the chance to play at Anfield when speaking to Sky Sports News after the match.
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"I'd like to thank the manager for giving me the opportunity also.
"It's great to be here and it's a world-class club. I have world-class players with me like Luis Suarez, Steven Gerrard, not to mention all the other players, but in terms of me being here at this club, it's great."The former Chelsea forward also took time to praise his new strike partner Luis Suarez after the match, as the pair once again linked up impressively, both getting on the scoresheet in the dominant display.
Suarez took his tally for the season to 20 with his first half strike against Norwich, after a clever dummy from Sturridge, and the 23-year-old insisted the best is still to come from the pair.
"It's good to play with [Suarez], we've been training well together and I think it's only gonna be a matter of time before we gel properly," Sturridge said.
"At the moment it's going well but it's gonna get a lot better than this because we've only played with each other for a couple of weeks so we don't really know how each other play but it seems to be clicking.
"We work a lot on that [the dummy] in training and we've been doing it for the last six or seven training sessions since I signed, so we click.
"We get on very well off the field and on the field it's showing in our play also."