Marcus Bean extended the lead with a header midway through the second half and a Max Ehmer own-goal put the result beyond question.
Carlisle scored an injury-time consolation goal through Ehmer who followed up after Sam Walker was unable to hold a Tom Lawrence free-kick, but there was no escaping their defensive shortcomings which threaten to hurl them back into a relegation struggle.
Kavanagh said: "We can't go on defending like that. It's unacceptable.
"The players would be stupid not to realise the importance of the situation. The mindset of the group has to change. We've got to be critical of a performance like that.
"We have had the same back four since I came here, but I'm not making excuses. It was not a bad performance, but the result is terrible and we have got to bounce back.
"It's a huge test for the players and we need to bring bodies in. We have young players in key areas of the pitch."
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