Joe Willock struck twice, with Callum Wilson also scoring in his return from injury as Newcastle won the fourth round tie 3-2.
Howe said afterwards: "It was a tough game for us. Mentally, physically – you could see a few players were on the edge today. We’re delighted to get through.
"I thought it was going to be a difficult night before the game.
"(Birmingham scoring early) made it doubly difficult because the atmosphere in the stadium totally changed. We managed to get a foothold and did really well. At half-time it was about staying calm. I thought we did that a lot better in the second half."
On injuries, he added: "In the last couple of weeks we seem to have picked up a couple. It would be the last thing to derail us. We have such a small squad. Last season we had big numbers of players out and it disrupted us in the middle of the season.
"We were forced to take Dan Burn off. It was something with his groin. Fingers crossed it’s not too bad."