The England international, who joined the former from the latter in January this year, spent four years at Stamford Bridge but failed to establish himself as a regular starter.
However, Sturridge, who has 10 goals in all competitions for Liverpool this season, feels there is more pressure to win silverware at Anfield due to the size of the club.
"This club is more of a pressure cooker than Chelsea," he told ESPN.
"(There) we were challenging for titles and the expectation from the fans and a lot of expensive players get bought and you're fighting for your place. But I think as a club, (Liverpool) is bigger, the history of the club and the way the fans want success."
Sturridge also dismissed allegations of being a self-centred player while at Chelsea - an accusation often levelled at him earlier in his career.
The 24-year-old explained: "The selfish thing - people at Chelsea have an opinion - and everyone's entitled to their opinion, but for me I was never given an opportunity there.
"I'm only on for five minutes, I've got to try and do something. I've got to try and shoot.
"People have an opinion of me, (saying) 'Daniel Sturridge this, Daniel Sturridge that' and I'm selfish and this and that, but for me I've always tried to help the team win games and here at Liverpool I always try and sit on my opponents and I'm not a selfish player.
"I'm not a selfish person. People who meet me here and management understand exactly where I'm coming from."
