Following City's strong showing at Shrewsbury Town on Saturday, Parkinson's men enjoyed the better of the game at Coventry's Ricoh Arena but still lost due to substitute Andrew Rose's winner for the Sky Blues just before the hour mark.
Parkinson said: "We are bitterly disappointed not to come away with anything from this game. There were so many things we did well tonight (Tuesday).
"We have looked in control for the vast majority of the game, certainly in the second period, but we've got punished for one moment out of the blue.
"We've shown great energy and great control on the ball to get ourselves in some promising positions - it was just that final pass or finish that was missing.
"We kept driving forwards and pressing them high, showing great energy levels, but we just had to kill them off when we had our chances.
"We have been unlucky in front of goal over the last two games but we have to start making our own luck."
City's attempts to get back in the match following Rose's opener were dealt a blow when Steven Davies was dismissed for apparently kicking out at Coventry defender Jack Stephens eight minutes from the end of normal time.
The nature of Davies' sending off means the striker is now scheduled to miss City's final three games of the regular season.
Parkinson added: "I've not seen the incident again but Steven knows that he has to keep his cool in those situations.
"Even with ten men though, I thought were excellent and still able to create opportunities to get back in the game."
After two frustrating away games in a short space of time, City will look to respond in a positive fashion when they entertain promotion-chasing Walsall at the Coral Windows Stadium this Saturday.
Parkinson continued: "We have a good opportunity to bounce-back this Saturday when Walsall come to town.
"You sometimes get periods in football when you don't perhaps get what you deserve but we have to concentrate on keeping our performance levels high.
"It will be great to get back in front of our own supporters at the weekend. They have backed us superbly in these last two games on the road.
"They have come out in their numbers and I thank them for their support. We are as disappointed as they will be that we head back to Bradford tonight with nothing."