Parkinson's men showed ample spirit to scramble back from a lacklustre performance in the opening half and the blow of conceding three Crewe goals to secure a hard-fought draw.
City's chief was understandably underwhelmed by his team's efforts in the first forty-five but felt the Bantams did more than enough after the restart to warrant something from the game.
Parkinson said: "I was disappointed with our performance in the first period.
"I felt defensively we were a bit disappointing today.
"Some of our decision-making at the back wasn't as good as it should have been.
"It was nothing to do with a lack of commitment or effort - we have that in abundance - it was just a lack of the usual calmness we normally show at the back.
"We lacked intensity in the first half and we weren't positive enough.
"Our first thought was to go backwards rather than forwards.
"We changed a few things around at half time and I felt we were great in the second half and showed how we can play.
"We have always had a sort of mantra here ever since I've been at the club that however we play and whatever the score, we have to make sure that the opposition back four is put under pressure.
"I think you can say that after the second half performance."
In a topsy-turvy second period at Valley Parade, City twice had to come from behind to collect a share of the spoils from the game.
Despite dominating the early stages after the break, City found themselves two down thanks to Uche Ikpeazu's second of the match.
Even when James Hanson and Gary Jones's quick-fire goals had drawn the Bantams level just before the hour mark, Parkinson's men still had to fight back once again when Mathias Pogba re-established the visitors' lead with just twelve minutes remaining.
Parkinson said: "When their second goal went in, I was still quite calm because I still felt we would score given the way we had begun the second period.
"We had completely dominated the start of the second half and had some great chances, so that gave me belief we could still score in the game.
"I knew if we continued in the same vein that we had started in after the break, the goals would come.
"Obviously they did through James (Hanson) and Gary (Jones) but unfortunately they have then got their third one.
"That goal was a real blow psychologically for the team but we responded great again."
The wet and windy conditions at a damp and cold Coral Windows Stadium certainly didn't make things easier for City but Parkinson wasn't prepared to use it as any sort of excuse.
Parkinson said: "It was tough, very tough out there, but you have to adapt. It was like this for most of the country. This is part and parcel of playing football in England.
"I felt Crewe adapted to the weather conditions very well in the first half.
"Crewe have this reputation for being a nice footballing side but they've looked at the weather conditions today and gone with two powerful forwards up top.
"They played to the conditions well in the first half, something I felt we didn't do, but we managed to change that in the second half.
"With the tricky conditions against us to begin with, I was toying with the idea of switching us around if we won the toss so that we had the wind in our favour in the first half. The players like attacking to our fans (the Kop) in the second half though, and I know the supporters do too."
Parkinson chose to hand an instant debut to Matthew Dolan in the Crewe fixture after the midfielder's loan move from Middlesbrough had been confirmed earlier in the day.
The Bantams chief added: "I like Matty as a player and I thought he was excellent in the second half.
"We seemed to get the ball more to him in the second half and he seemed to understand a bit more how we play.
"As the game opened up, he got more of the ball and he passed it well.
"Him and Gary (Jones) seemed to have a good balance in there (the midfield) in the second half."