Sturridge celebrated his first appearance in seven weeks following an ankle injury with his side's final goal, while Uruguayan Suarez scored his 21st and 22nd goals of the season as the Reds beat Stoke at the Britannia Stadium for the first time in the Premier League.
The win lifted Liverpool back into the top four with 42 points, five behind leaders Manchester City who win 2-0 over Newcastle.
Yet Rodgers acknowledged that if they are to remain in the Champions League places they need to improve on a defensive effort that allowed Stoke to come back from two goals down to draw level at 2-2 before halftime.
Lax defending had allowed former Anfield players Peter Crouch and Charlie Adam to cancel out a Ryan Shawcross own goal and Suarez's first.
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