Everton midfielder Lee Carsley says Liverpool boss Rafael Benitez's comment that the Toffees are a small club was a "stupid thing to say".
Benitez said after Saturday's goalless Merseyside derby: "When you play against the smaller teams at Anfield you know the game will be narrow."
But Carsley said: "We've beaten them this season so if we're a small club I hope other small clubs beat them.
"We feel insulted by what he said. It's a stupid thing to say."
Carsley added: "I can understand him being frustrated afterwards, but anyone who watched the game will know Andy Johnson had the best chance.
"We could quite easily have won 1-0, which we've done to other teams in the past - so he should keep his opinions to himself."
Everton chief executive Keith Wyness had already expressed his disappointment at Benitez's comments.
Wyness said on the club's website: "Benitez is in a minority of one in believing Everton is a small club.
"Somehow we just expect more of a Liverpool manager."
Benitez was angry with Everton's tactics in holding the Reds to a stalemate at Anfield as Liverpool fell further behind second-placed Chelsea.
"When you play against a big club, a draw is sometimes a good result"
Liverpool dominated possession in the 205th derby but failed to find a way through a stubborn Everton resistance.
He said: "There was only one team that wanted to win and one team that didn't want to lose, they had nine men all the time behind the ball.
"When you play against a big club, a draw is sometimes a good result."
Everton manager David Moyes was not happy with Benitez's comments.
"I would not say that about any football club anywhere," said the Everton boss. "I am disappointed that has been said.
"There is no doubt we are in the shadow of Liverpool, but we are doing our utmost to compete with them."
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Moyes felt his side were unlucky not to have gained their second win over their neighbours this season.
He said: "We've taken four points off Liverpool this season, so we must be doing something right.
"There's a difference of about £100m in spending between the two clubs, but we are doing our best to bridge the gap. I would have liked to come here and put on a bigger show, but it's not an easy place to get a result and we've not done bad.
"We could even have won the game with a bit more luck."
Wyness however, was not as forgiving and felt Benitez's comments were inappropriate.
He added: "It is disappointing to hear such an unnecessary comment at the conclusion of what was such a splendid local derby."