Crewe players and manager Dario Gradi have responded to comments made by Accrington manager John Coleman after the Alex won 2-0 at the Crown Ground.
Coleman said his team "should be beating teams like Crewe at home".
Gradi told BBC Radio Stoke: "I think he preceded that by saying 'no disrespect' and when people say that, you can be sure they'll show disrespect."
Keeper Steve Phillips added: "He lives in a dreamland if he thinks he should be beating anybody in this division."
Early goals from AJ Leitch-Smith and Byron Moore gave Crewe their first league win away at Accrington since January 1961.
"Everybody can beat each other [in League Two] and I thought it was a disrespectful old cliche," said Phillips, who kept his third clean sheet in six matches on Saturday.
Gradi added: "I'd be pleased if all the other managers of the teams we play all feel the same way. That will hold us in good stead, I would have thought."
The Alex, who have won four of their last five league matches, face Port Vale in a local derby at Gresty Road on Saturday.
BBC Radio Stoke will have live commentary of Crewe v Port Vale on 94.6FM from 1500 BST on Saturday, 24 September.