Swansea lifted the trophy last season but were knocked out in the third round on Wednesday after going down 3-1 at St Andrew's.
Michael Laudrup's men had created a number of chances in the first half without taking them and Monk accepts that Birmingham were superior after the break.
"We got what we deserved in the second half," Monk told the South Wales Evening Post
"In the first half we should have scored a few goals and it would have been a different game then, but we didn't when we definitely should have had one or two and ifs and buts don't count.
"In the second half they were the better team, we made some silly mistakes and got punished.
"It must have looked from the side of the pitch as if their first goal affected us, although it didn't really.
"The story of the game was that they took the chances they had and we didn't.
"We didn't deserve it from the second half so what can you say?"