The Liverpool skipper lasted just 38 seconds as a second half substitute in the 2-1 defeat to Man Utd before being red-carded for a stamp on Herrera.
"Steven probably watched the first half and saw us not make a tackle and there was probably some frustration in there," admitted Rodgers.
"He is a wonderful captain and came on hoping he could influence the game, but that was probably not the way he would have liked it.
"It is big of someone when they do get sent off to come out and apologise. He was probably frustrated watching us in the first half, we didn't make a tackle. He was man enough to come out and apologise.
"I won't criticise him. He has been brilliant since I came here. We will move on."