Despite leading twice during the match at the Coral Windows Stadium, Parkinson's men lost out to 'Boro thanks to two superb second half strikes from visiting attacker Luke Freeman.
The loss denied the Bantams the opportunity to make it three consecutive victories following earlier wins over Port Vale and Milton Keynes Dons at Valley Parade.
After City's recent home triple-header, Parkinson's squad are now set to hit the road again with back-to-back away games in the space of four days.
The Bantams travel to promotion-chasing Brentford on Saturday before visiting Colchester United the Tuesday after.
Parkinson said: "I think we wasted a good opportunity on Saturday, especially after the momentum of the two previous wins (over Port Vale and Milton Keynes Dons), and we have to regroup and go again.
"We have to pick ourselves up, dust ourselves off and go into these two away games with confidence.
"We have to be ready for them and I'm sure we will be.
"They are two tough games but we will be ready for the challenge.
"We will have to be resilient. We will be really focusing this week in training on what exactly will be required."