After conceding Chigozie Ugwu's eventual match-winner during a slowing opening to the contest, City dominated proceedings, especially in a one-sided second period, as they looked for a way back into the match.
Despite a couple of close moments though, Parkinson's men couldn't prevent a frustrating loss at the hands of Gary Johnson's Glovers.
The Bantams' match at Yeovil came at the end of an eventful week for City which included playing 80 minutes with ten men against Rochdale last Saturday, securing a trip to Chelsea with a thrilling win over Millwall on the Wednesday, not to mention the long trip down to Yeovil itself.
Given the energy-sapping efforts of the last few days then, Parkinson praised City's ability to keep pushing back Yeovil time after time as the minutes ticked by.
Parkinson said: "It has been a testing week for the lads - there's no doubt about that - but we still found it within ourselves to go again after conceding Yeovil's goal.
"We started slowly in the game and we weren't quite at the races.
"We knew that the start would be key as Yeovil would come out quickly at us given we'd played on Wednesday.
"We got punished for it with the goal but I felt we played well after that without really showing that quality required in and around the final third.
"We had plenty of possession and we deserved something out of the game.
"It is just that slow start that has cost us.
"I can't remember them having any real chances in the second period - we just couldn't produce that real quality cross or quality final ball to finish things off.
"A lot of our play deserved an end product but we haven't worked their 'keeper enough for all the dominance we had.
"Their goal has obviously given them a confidence boost but the way the lads responded was tremendous. They gave everything for the shirt.
"We've had a tough week in terms of the games we've played and the travelling we've had but we move on now and look forward to a terrific match against Chelsea next weekend.
"We will have a review of the game on the way home tonight and then we'll be ready for an exciting week for all at the football club."
This Saturday's match is scheduled to be the last of the current loan periods for both Andy Halliday and Francois Zoko.
Parkinson is keen to keep hold of the duo a bit longer, however, while Ben Williams, whose deal runs out at the end of the month, should certainly be sticking around for longer according to the City chief.
He added: "I would like to keep them both if we can.
"I thought Zoks (Francois Zoko) did well when he came on.
"He has been unlucky not to feature more but Billy Clarke, Billy Knott, Jon Stead and James Hanson have been doing well recently in those attacking positions.
"We will have discussions with both players and their clubs though and we'll wait and see.
"We have an agreement in place with Ben that he will stay with us for the rest of the season and the year after that.
"Ben is a good goalkeeper and a good character to have around the building."