Premier League - McLeish cheered by battling Blues
Jean Beausejour gave the Blues the lead with a header on 17 minutes at Goodison Park before John Heitinga's screamer levelled things up midway through the second half.
The hosts dominated large periods of possession and looked the more likely to score but they could not find a way through a stubborn Birmingham defence.
"I think that is an apt way to describe it - a battling point," McLeish said.
"We started very brightly and got the opening goal. Then the players showed that tremendous resilience that they have."
He added: "We tried to be a little bit more predatory, but we never really had the composure in terms of the passing in the second half.
"But sometimes you need to get points in an ugly fashion."
With Tim Cahill and Marouane Fellaini missing through injury, Everton's lack of creativity was evident, a situation made even worse early in the game when midfielder schemer Mikel Arteta was forced off with a hamstring problem.
Asked how Arteta was, Toffees manager David Moyes said: "I don't know, I just saw him come off.
"Obviously it looks like a hamstring injury but I haven't had a chat with the medical team yet to see what they think.
"It was a big blow for us because we needed some creativity and I knew that if we didn't have him, we would be struggling to create too much.
"Leon Osman did, but we were struggling otherwise really to make anything happen.
"It was a bit frustrating. We didn't play well enough probably to win the game, but we had a few half chances."