In addition to the promoted trio,
Sunderland lost 1-0 at Brighton
to ensure that half of the eight Premier League sides in action on Tuesday were defeated.
CARLING CUP CROWDS
The average attendance of Tuesday's 16 Carling Cup ties was 7,631, with only three games attracting gates of more than 10,000
"I'm not disappointed to be out. The competition is not a priority for us," added Warnock, who made eight changes to the side that beat Everton on Saturday.
"If I can't get motivated for the competition I can't blame the players if they can't."
But Rochdale manager Steve Eyre queried Warnock's opinions.
"Neil didn't say before the game that he doesn't take it seriously," he said.
"To field a front line that has Adel Taarabt and Jay Bothroyd tells me it was taken quite seriously.
"It's still a fantastic competition. Wembley [venue for the Carling Cup final] is an amazing place to play football."
Norwich boss Paul Lambert, who made 11 changes to the side that drew with Stoke on Sunday, did not criticise the Carling Cup but admitted that the battle for Premier League survival played a part in his team selection.
"The season is too hard to keep going with the same lads," Lambert told BBC Radio Norfolk.
"We're new to it [the Premier League] and we have to keep rotating in certain games. We need everybody and if we do that we've got a chance [of staying up]."
Five more Premier League teams open their Carling Cup campaigns in the second round on Wednesday and Thursday, with the seven top-flight clubs taking part in European competitions this season entering in round three.
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