Chuks Aneke and Mesca were on the score-sheet as Crewe heralded the New Year with back-to-back victories, while Tom Lawrence replied for the Cumbrians with a fine free-kick.
Crewe carved out enough chances to win two games and Carlisle were lucky to still be in the game at the turnaround after Aneke hit the woodwork and Inman spurned a chance of his own making when clean through.
Kavanagh has urged his players to pick themselves up ahead of the trip to the Stadium of Light.
"There's a big game coming up and it's important we dust ourselves down and get back on our bike again," Kavanagh said.
"That wasn't good enough and we were way off the pace in the first-half.
"We lacked energy, tempo and confidence and I'm gutted for our fans.
"It's slow progress for us at the moment and we seem to take two steps forward and one step back."
- Sports & Recreation
- Chuks Aneke