The 23-year-old scored on his debut in a comfortable win against Mansfield Town in the FA Cup third round, before striking again in a 2-1 loss to Manchester United at Old Trafford.
Sturridge came on as a second-half substitute against the Red Devils and made a noticeable impact, inspiring Rodgers’ men to a much-improved performance in the final 30 minutes.
The Liverpool manager has been forced to rely on Luis Suárez to score the bulk of his side’s goals this term, but the Northern Irishman expects his new £12m signing to help share the workload.
“He gave us a different dimension, real pace, working on the shoulder of the last defender and every time he’s in the box you just sense that he can get a goal,” Rodgers told Liverpool’s website.
“I think good players enjoy playing with each other.
“With Daniel coming in I think everybody recognises we have a good player who is 23 years of age and has his best years ahead of him.
“You see him [against Manchester United] – and he’s not even fully fit yet – he’s going to be a real handful.
“For us going forward, he and one or two of the other players are going to be the real difference.”
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