The Red Dragons suffered their first league loss since the trip to Stoke on Oct. 18 as Kyle Joseph and returning substitute Oli McBurnie sealed the Tigers a 2-0 win at the MKM Stadium.
Kieffer Moore wasted a glorious chance for Wrexham in the opening period and saw a second-half penalty saved by Ivor Pandur, but few would argue that Hull did not deserve Wednesday's victory.
Even Parkinson praised the hosts, having watched his side stumble from the stands and play particularly poorly in the first 45 minutes.
"We just weren't at the levels tonight and I've got to look at that -- my part in it, all the staff will, and the players themselves," the Wrexham manager said.
"But we'll do that together. The lads have given us a lot but tonight we were below the level, and we'll come out ready for action at the weekend."
Parkinson said he let the players know what he thought of the performance in the dressing room after the match, having given them Thursday off to recover from the journey back to north Wales.
"We've just had an honest chat with the lads," he said. "We just weren't where we needed to be tonight and we've got to be honest about that.
"It's very rare in my whole time at Wrexham to have a 45 minutes that was so unlike us.
"Tonight the first 45 minutes was certainly one of those performances, but against a good side as well. Give them credit, they were excellent.
"We will look to respond, of course. That's what football's all about.
"We'll be a bit flat tomorrow because we don't like losing. Nobody does in football, but we'll work together as a group, and we'll look to putting up a good performance on the weekend."
Wrexham, who now sit 14th in England's second tier, will attempt to bounce back at home to Watford on Saturday
Information from PA was used in this report.
