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Following Friday's 1-0 defeat at Bramall Lane, the Reds boss pointed to Wrexham's memorable FA Cup battles with Sheffield United in the 2022-23 campaign as the benchmark.
The Reds, challenging for the National League title, were huge outsiders but on course to cause a huge shock before conceding a late equaliser to draw 3-3 at The Racecourse in the third round while the Blades, on course for the Premier League that season, scored two late goals in the replay to progress despite being given a run for their money by the north Wales outfit.
Parkinson argued that a fifth tier side full of underdogs had shown more courage and competitiveness against superior opposition than his current team managed.
"First half we were way off it," he said, with striker Ben Brereton Diaz's 30th minute goal the difference between the sides.
"I said to the lads in there that we played Sheffield United when we were in the National League at home, 3-3 in the FA Cup and went toe to toe with a top Championship team, top of the table.
"Came here 10 days later, everyone thought we'd had our chance and we'd just roll over and get beat four or five.
"We went toe to toe with them again, missed a penalty and put in an unbelievable performance.
"So with a lot lesser team, we did a lot better against a better side and we've got to look at reasons for that because in that first period we were second to the duels."
Parkinson admitted his players’ effort and desire were “not where they need to be” in the opening half and although there was an improvement after the break, they slipped to a fourth league defeat in their last seven matches and remain 17th in the table.
“We were slow on the ball and our intensity levels weren’t where they needed to be. Second half, we did loads better," he said.
“But whatever system you play, whatever personnel you play, the team has got to represent the town in the way it has done for the majority of the last five years.
“I think this season we’ve had some really good performances, but I just said to lads in the dressing room, I don’t feel we’ve got a consistent level of effort and desire every week, and that’s what our fans are used to seeing.”