The Toffees lost the game 1-0 following a goal by Dirk Kuyt.
Both Liverpool defender Sotirios Kyrgiakos and Everton midfielder Steven Pienaar were sent off in the game.
He said: “I think there have been lots of derbies very similar; quite feisty and that’s why fans like them because they sometimes have a little bit extra in them.
“The first sending-off (Kyrgiakos) was a two-footed tackle, both feet off the ground. Fellaini has been for an X-ray but we think it is clear, which is good news.
“I’ve no complaints about Steven’s sending-off as there was a tackle earlier in the game where he might have been fortunate to stay on.
“I thought we certainly didn’t deserve to lose the game. We might not have deserved to win it but we shouldn’t have lost it.
“We didn’t create enough chances with the extra man but, saying that, Liverpool didn’t either and their goal came from one set-piece – which in the past would have been us that might have done that but it was Liverpool today.”
