The Merseyside outfit welcomed Ligue 1 champions Paris Saint-Germain to Anfield on Tuesday night in their opening group-stage fixture.
Sturridge was handed his first start in the Champions League despite moving to Liverpool FC from Chelsea FC under Brendan Rodgers in January 2013.
The 29-year-old, who was also making his first start of the season, broke the deadlock in the 30th minute with a powerful header.
James Milner doubled the home side’s lead from the penalty spot before PSG halved the deficit before half-time to offer the visitors some hope.
Sturridge produced a tenacious performance as the England international deputised for Roberto Firmino in Jurgen Klopp’s starting line up.
Kylian Mbappe equalised for PSG with six minutes left to play before Firmino came off the bench to net a dramatic winner in added time.
Sky Sports pundit Rosenior believes Sturridge will play a key role in Liverpool FC’s bid to win the Champions League.
“If you’re looking at winning a Champions League or Premier League, you want strength in depth, and Sturridge will be a key part of that this year,” Rosenior told Sky Sports.
“He looked lighter and fresher in pre-season.
“Maybe he’s gone away on loan and seen Liverpool playing in the Champions League final and said: ‘You know what, I want to be part of the Liverpool squad’, and what’s in his favour is his ability as a player has never been in doubt.
“It’s just whether he can maintain his form and stay fit.
“If he stays fit, they’ve got another striker who two or three years ago we were talking about being absolutely world class, almost winning the title.”
The Reds haven’t won the Champions League since 2005 when the Merseyside outfit beat AC Milan on penalties.
Liverpool FC have lost to AC Milan and Real Madrid in subsequent Champions League finals in 2007 and 2018.
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