Shelvey seized possession but as the ball broke free he launched himself at Evans and was shown a red card. Rodgers, however, said both players should have been given the same punishment for that duel.
"Jonjo Shelvey, if he gets sent off then Jonny Evans has to go as well," Rodgers said. "I think both players' feet are off the floor."
Ferguson was involved in a heated exchange of words as Shelvey left the pitch.
"He was trying to blame me, I suppose," Ferguson said. "Once he looks at it he can apologize if he likes."
Shelvey, though, mainly only apologized to the fans.
"No way was I pulling out of that tackle in a game of that importance. Im sorry," Shelvey wrote on Twitter. "I have also apologised to sir Alex, just where I come from people don't grass people up to get someone sent off."
Even with a numerical disadvantage, Liverpool continued to pressure United and Suarez drew Lindegaard into a low save from his free kick.
And at the start of the second half, Gerrard received a diverted ball in the area and volleyed home left-footed in front of the Kop.
The lead only lasted five minutes, however, as Shinji Kagawa laid the ball off for Rafael to curl left-footed over Reina and in off the far post.
But, even with a man down, Liverpool pushed for a winner with Suso having a shot tipped over by Lindegaard and Suarez continuing to trouble the United defense.
United began to take more control, though, and the winner came from Liverpool giving away possession on the halfway line.
Daniel Agger and Johnson collided to allow Valencia to race 50 yards into the area and, although Johnson got back, he brought down the Ecuador winger.
Van Persie drilled home despite Reina diving the right way and getting a hand to the ball.
