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.
“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.”