Middlesbrough boss Tony Mowbray has warned his players they cannot afford to leak goals if they are to fight their way back into the Premier League.
Boro led twice at Birmingham on Friday night, but ultimately returned from the midlands empty-handed after conceding three times.
Mowbray said: "Let's not criticise anybody, it is what it is and the team have been great this season.
"With performances like we have had in the last couple of away games, we will win more than we lose.
"But we are here to try to get out of this league and win football matches.
"We have to understand the urgency of it, and we can't lose three goals of that nature."
The Bantams, who take on Port Vale on Tuesday in the Johnstone's Paint Trophy northern section quarter-final, are unbeaten in eight cup matches this season.
They play Arsenal in the quarter-finals of the Capital One Cup next week and drew with Brentford in the third round of the FA Cup on Saturday.
Parkinson said: "In the Johnstone's Paint Trophy in the early rounds the crowds are low and you have to make sure the motivation and the attitude of the team is right, but once you get through a couple of rounds it does become a more exciting proposition with the chance of a trip to Wembley.
"So if we can get a result at Port Vale we're two rounds off going to Wembley, so it's a big game and we're in a lot of competitions at the moment and we're enjoying it.
"You've got to enjoy runs like this. It's also given me a chance to utilise the squad to it's maximum, which is very important because we haven't got many reserve fixtures, so lads who haven't played are getting match fitness in first-team games.
"We've said from day one that the league is our priority, but confidence is a great thing in football and in the FA Cup replay with Northampton the lads have shown their spirit to come back in that and against Bristol Rovers in the league last week when we were down three times in the game, but kept coming back.
"That kind of desire and spirit in the squad is evident every week and we've got to keep it there because that can take you a long way and it certainly has so far this season."
