Lee Carsley claims Everton's players feel 'insulted' by Rafael Benitez's comments which have sparked a furore on Merseyside.
Liverpool manager Benitez referred to city rivals Everton as 'a smaller team' following Saturday's Premiership stalemate at Anfield.
That prompted an angry response from Everton supporters, and led to chief executive Keith Wyness expressing his club's disappointment 'to hear such an unnecessary comment'.
Wyness added: 'I suspect he is in a minority of one in believing Everton is, in any respect, a small football club.
'Somehow we just expect more of a Liverpool manager.'
Midfielder Carsley, who played the full 90 minutes, feels Benitez should learn to 'keep his opinions to himself'.
'We've beaten them and drawn with them this season, so if we're a small club then I hope other small clubs can beat them,' snapped back Carsley.
'We feel insulted by what he said. It's a stupid thing to say.
'I can understand him being frustrated afterwards, but anyone who watched the game will know [Everton's] 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.'
Asked whether Benitez should apologise, Carsley replied: 'I don't think he will - but then I don't think he should have to either. It's his opinion, one of those things.'
Hammering home a point, though, Carsley added: 'We were pleased to get a point on Saturday.
'Derby games are tough, but we've taken four points off them this season - so we've done well.
'We played the same system on Saturday as we did when we finished fourth a couple of seasons ago to claim a place in the Champions League.
'For a small club, that's not bad.'
Benitez launched a explanation today which claimed that he was referring to all clubs outside the top four who come to Anfield, and not just Everton.
Benitez said: 'It's easy for me to explain what I've said. I've read lots of comments from Bill Shankly over the years where he's made comments which compared Liverpool as a club to other teams. I've done it on this occasion.
'I'm the manager of Liverpool and I was simply comparing our club to most other clubs who come to Anfield. We are in a position where we are trying to compete with Manchester United, Chelsea and Arsenal, while for other teams and managers that's more difficult.
'The top four are considered the biggest clubs in the Premiership, and even managers from other teams accept it's different for them when they play against the bigger teams. That's what I was saying.'