Nugent saw red in stoppage-time when he tried to wrestle a dead ball from Stephen Gleeson.
It compounded a frustrating afternoon for Boro, who could have gone top after Brighton’s draw at Derby.
“I’m disappointed because it isdifficult playing at home always trying to win games, against sides that are wasting time,” said Karanka. “So you can understand his (Nugent’s) frustration, but you have to learn not to do that. He knows he’s made a mistake but it’s up to the other players on Tuesday to make up for this.”
Boro started brightly and missed a number of chances in the first-half, with Grant Leadbitter hitting the post.
“It was frustrating because we couldn’t get that first goal,” added Karanka.
“We should have scored four goals in the first half. We created chances but didn’t take them.
“The conditions with the wind and the rain didn’t help but we still created a lot of chances.
“Birmingham created chances too, but I sent the team out with the message not to make any mistakes because the conditions weren’t easy.
“We had to concentrate even more because of that because one mistake would have decided the game.”
Birmingham were good value for at least a point as they missed late chances at the other end.
Middlesbrough: Konstantopoulos, Nsue, Ayala, Gibson, Friend, Clayton; Leadbitter, Stuani (Forshaw 79), Downing, Adomah (Fabbrini 87); Nugent. Unused substitutes: Amorebieta, Garcia, Mejias, Kalas, Zuculini.
Birmingham City: Kuszczak, Eardley, Morrison, Spector, Grounds, Gleeson; Kieftenbeld, Maghoma, Shinnie (Davis 71), Gray (Halford 86); Vaughan (Solomon-Otabor 80). Unused substitutes: Legzdins, Lowry, Caddis, Brock-Madsen.
Referee: Darren Bond (Lancashire).
Man of the match: Jacques Maghoma.