The Uruguayan striker scored twice as the Reds dominated the second half against Roberto Martinez's men to post only their fourth league win at Anfield in 2012.
But Rodgers believes the result was a product of his side's collective performance, rather than individual brilliance.
"It’s not just Luis Suarez. Luis Suarez finishes off the great work," he told reporters.
"Don’t get me wrong, he’s a wonderful striker and he gets paid a good sum of money to score goals but so do lots of other teams.
"Lots of other teams have strikers that are the pinnacle and finish off a lot of good work. We’re very much a team and Luis is a very big part of that.
"His first goal was a wonderful finish, great weight of pass by Raheem [Sterling] and he finished it great and the second one is a lovely pass from Jose Enrique and a nice little off-the-shoulder run and finish.
"He’s a master marksman, absolutely outstanding and obviously we’re thrilled to have him but the ethos is very much along the team and I thought the team was excellent today."
Despite insisting the 25-year-old is ably assisted by his team-mates, Rodgers did admit he is keen to source attacking reinforcements in January.
"We’ll see what January brings," he said.
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"I’m not going to sit here and say we’re going to get five/six players in it doesn’t work that way.
"We know it’s going to be very difficult this season in terms of transitioning the group but we’ll get some support in and the players that we’ve got we’ll work with them and see where it takes us."
The Northern Irishman chose to withdraw Suso with just 30 minutes on the clock, but revealed that the substitution was a tactical one, rather than enforced by injury.
"[It was] just tactical," he added.
"I felt that the organisation at the front end of the field wasn’t as what I wanted really. You make a decision in the game you can either let it run but I always try to use my intuition and what I feel is best for the team at that moment.
"He had some nice touches, he nearly scored but that’s a part of the game. I just felt I’d flip the triangle around, we were playing two and one and I felt that it wasn’t so good for us when we didn’t have the ball."
The 39-year-old also compared Jose Enrique's switch from full-back to the left wing to that made by Gareth Bale following his move to Tottenham.
"He’s a terrific talent. I just felt pushing that bit further forward; you look at Gareth Bale, he played a lot at left-back and pushed forward one and really showed his strengths," he continued.
"Jose is someone I think can do that role with his power and pace, I said to him yesterday [about] the number of goals he and Raheem can get if they get inside the frame of the goal."