Birmingham admitted he was slightly annoyed at the manner his men allowed Conner Grant to pull one back for US Portsmouth a minute past the hour mark.
But overall the Deans boss was satisfied with his side's efforts on a 'heavy' Five Heads Park pitch, which had passed an afternoon inspection in order for the match to go ahead.
Birmingham said: ‘Especially (in the) first half, we were really good. We played at a high tempo, moved the ball and we pressed them particularly high as well.
‘I’m not going to lie, the pitch was extremely heavy, it was borderline - both sides looked at it and wondered how it (the game) had been given the go ahead. It was really heavy and carved up very easily.
‘We spoke about it before the game, we’ve been a bit toothless in the past few games - to be honest the lads have said they’d been a bit toothless.
‘We knew we had to give them the utmost respect and I think our first-half performance showed how much respect we gave them.
‘It’s been a little bit inconsistent the past five or six games so it was nice to get the three points.
‘We had chances, we could have won by more, I’m very disappointed with the goal they scored, but that’s really about the only sour note I’ve got.’