The second-placed Deans were held at Five Heads Park by place-below Brock in a fixture lacking in any real clear-cut chances.
Birmingham felt the fact the sides meet in the reverse match in the league did not help matters – and he conceded the only real 'winner' on the day was the ‘lively playing surface and the conditions’.
Birmingham said: ‘Both teams huffed and puffed, worked hard and that was really about it. Both teams had a game plan, we had a game plan set up to stop Brockenhurst, they set up to stop Horndean and it worked.
‘I think overall the pitch and the conditions were the winner yesterday. It was a very lively pitch, the wind was very, very strong.
‘I don't think it was a fear of losing - you shouldn't fear losing anyway because it's part of the game - it probably doesn't help when you've got each other back to back. It's hard to prepare for that because you could be on fire one week and the next week you're not.’
In a game of minimal goalmouth action, Horndean stopper Leon Pitman had to get down to keep out Connor Ings' low drive with relative ease on 25 minutes.
At the other end, the Deans' leading scorer Connor Duffin sent a couple of decent openings wide of the target.
The stalemate means Horndean stay three points and a position above third-placed Brock in the table, although they have played two matches more.
Birmingham added: ‘We saw quite a bit of Brockenhurst yesterday, they saw quite a bit of Horndean - Pat (McManus; Brockenhurst boss) is a top man, he gets his team well drilled, well set up and we struggled to break them down - the same as what they struggled to break us down.’
Horndean travel to face Brockenhurst in the New Forest for what will be the third meeting between the teams this term next Saturday.