At the end of a week during which the Magpies restored pride with a battling point against Arsenal, it looked as though they were heading for a draw until Habib Beye turned up at the near post in the final minute to head Emre's corner past Maik Taylor.
The goal - Beye's first for the club to end a drought dating back to January last year - secured Newcastle's first league win in seven attempts and further eased the pressure on a manager who just a few days ago was joint favourite with the bookmakers to lose his job.
Allardyce said: "It is a really, really big three points. Nothing else really mattered today but three points, and we got them.
"We have worked very, very hard over the last seven days - Blackburn and then Arsenal and now Birmingham - and now finally got what we deserved.
"Birmingham, for us, is a winnable game. It would have been a huge disappointment had we not won this game today. I would have had to say 'this is not good enough'.
"As spirited and good a performance as Birmingham put up today, by the amount of dominance we showed in the first half - even though we did play a game in midweek and they did not - we should have put those chances away and put it beyond Birmingham."
As ever with Newcastle, the win was far from straightforward after they 'gifted' striker Cameron Jerome the opening goal with just nine minutes gone.
They eventually levelled from the penalty spot on 36 minutes after Obafemi Martins picked himself up from Mathew Sadler's challenge to score his seventh goal of the season - and they belatedly took charge.
However, substitute Emre breathed new life into their late assault - and after seeing strong claims for a penalty waved away when Jerome appeared to block his late free-kick with his arm, he curled the perfect corner to the near post for Beye to head past Taylor.
Allardyce said: "We have climbed up to where we ultimately had to get to today, and that was the win on the back of some good performances.
"Great credit has got to go to the lads for today's monumental effort. The huge disappointment of going 1-0 down to such a sloppy goal again was going to be a big 'ask' for the nerves.
"But the fans got behind us - and we kept on going, made the substitutions and kept on going, kept on going; then a quality ball and a quality header put us three points on the board that we so richly deserved."