Sturridge equalled former Manchester United striker Ruud van Nistelrooy's record of scoring in eight consecutive Premier League matches as he helped push fourth-placed Liverpool within four points of leaders Chelsea F.C.
"He's a natural goalscorer," Rodgers told reporters. "He looks like he can score in every single game.
"He's got the ability, he's got the quality and thankfully he plays for us here and has still got a lot of improving to do."
With title-chasing trio Chelsea F.C., Arsenal F.C. and Manchester City F.C. all having won on Saturday, Rodgers said the pressure was firmly on Liverpool F.C.
"It's the point of the season where it is all about winning," he added. "That's what professional sport is about at this level.
"Especially when you're up there challenging. When everyone wins the day before, even though you try to take that pressure off, mentally and psychologically there's maybe that feeling that you know you've got to win."
Liverpool F.C. looked to be heading for an easy day at Anfield after early strikes from Sturridge and Jordan Henderson had given them a 2-0 lead.
Quickfire goals from former Liverpool F.C. midfielder Jonjo Shelvey and Wilfried Bony levelled things up for Swansea before Sturridge netted again.
Bony replied with a 47th-minute penalty only for Henderson to grab his second goal.
England midfielder Henderson produced another eye-catching performance and Rodgers said he was pleased with the progress he had made this season.
"Jordan showed great leadership today," the former Swansea boss explained. "You could see him driving the team on.
"His first goal was an outstanding goal. We've been talking to him about getting up there (into the penalty area) because in training his finishing is sublime."