"At home in particular you always like to try and get a cushion of two or three goals, but it's not always meant to be and you can't win every game in style," he told MUTV.
The Reds went into the game on the back of their shock 2-1 defeat at West Ham. Ferdinand's younger brother Anton was on the scoresheet at Upton Park which added insult to injury for the United defender.
"Losing at West Ham ruined the Christmas period for me, especially as my brother scored as well!" he admitted.
"But you've got to take results on the chin sometimes and make sure you don't drop any more points in the next match.
"We didn't get the exact response we wanted against Birmingham [in terms of the performance], but most importantly we got the result we needed.
"If we'd have dropped points against them we'd have been in a bad position. But we're still there or thereabouts in the title race and we'd have taken this position at the start of the season."