Two headed set-pieces goals from Yeovil centre half Aaron Martin put the visitors in control early into the first period before Glovers striker Ajay Leitch-Smith made the points safe for the Somerset-based side with a fine finish in the second half.
City defender Rory McArdle did give the Bantams some hope when he pulled a goal back shortly after Martin's second of the game but Parkinson's side never really looked themselves throughout the contest.
This Saturday's Yeovil fixture was City's ninth game of the season already just under a month into the new campaign. Parkinson feels the Bantams' hectic early run of matches may have contributed to his side's low-key showing.
Next week will be the first week of the season for the Bantams without a midweek fixture and Parkinson says his chargers will benefit greatly from break in their busy schedule.
Parkinson said: "We were well below par - I think that was obvious for everyone to see.
"We conceded two poor goals from set-plays, which gave them a lift. Even though we got the goal back in the first half, I never felt we had enough about us today (Saturday).
"We lacked spark and we lacked energy.
"To be fair to the lads, they have been terrific so far this season but we can't deny that today, for whatever reason, was a poor performance.
"It is frustrating because I feel if we'd have played anywhere near like how we can play, then we would have got something out of the game.
"No matter what formation or system you play, the game is won and lost in both boxes and I felt Yeovil were better than us in that department.
"It is a shame because we normally pride ourselves over the past couple of years of doing well in this area but Yeovil were first to most balls today.
"We rested some of the lads on Tuesday (vs Oldham Athletic, Johnstone's Paint Trophy tie) with the aim of them giving us that spark this Saturday but they didn't seem to have it in their legs this afternoon.
"As a team, we gave an almighty effort in the Leeds and Rochdale games, and then we had to go again Tuesday at Oldham.
"To me, we looked like a team that might be ready for the break in fixtures that we will get this week. I think we need that break.
"Alan Sheehan had a bit of a thigh strain going into today, Matthew Dolan had to pull out of the warm-up, Filipe Morais pulled out this morning. I think these injuries are an accumulation of the start of the season we've had so far, maybe it has caught up with us a bit.
"We'll be having a head-count Monday/Tuesday to see who is available for selection for the weekend.
"We have to make sure that come next Saturday and Swindon Town we are ready to give a performance that better reflects how we have been so far this season."