Teddy Sheringham opened the scoring after 55 minutes but to their credit, City hit back and levelled via Jeff Kenna's first Premiership goal for seven years.
In tough, heavy conditions, spells of possession and clear-cut chances were at a premium.
"I don't think either side deserved to win the game," said Glenn afterwards. "A draw was probably a fair result.
"Our disappointment was that we were 1-0 up and that was a key moment in the game where we should have tried to improve our performance.
"If we had I think we would have won the game. We didn't do that.
"Be fair to Birmingham, it's a hard place to come and the crowd was loudest when we were 1-0 up. That lifted them.
"We're disappointed that we didn't lift our game at 1-0 up and not playing particularly well.
"Conditions meant it was hard to get the ball down and play, it was like a bar of soap sometimes. That suited their game more than ours.
"But sometimes it might have to be an ugly performance that gets you a win and that's what we were looking for."
Glenn Hoddle was disappointed we didn't go on to beat Birmingham City after going ahead in Saturday's draw at St Andrews.