Leeds United striker Patrick Bamford has been branded a "joke" for criticising Jesse Marsch's tactics in the defeat at Nottingham Forest.
Bamford said Sunday's 1-0 loss was "difficult" because Forest's centre-backs "just had me to concentrate on".
Marsch was sacked on Monday after seven Premier League games without a win.
"Keep it in the confines of the dressing room if that's the way you feel," Premier League title winner Sutton told BBC Radio 5 Live's Monday Night Club.
"He's unburdening himself of any responsibility. I don't like that.
"He's not daft - he knows the implications that it will have. It will be taken as a criticism of the manager and his tactics.
"He's a joke for bringing that into the public domain."
Bamford said in his post-match interview: "We needed more runners running past me to drag [Forest's centre-backs] out of position and create a bit more space.
"The whole game was literally two v one, which made it difficult, and unfortunately I couldn't find the answers to solve that."