The Blues benefitted from a glaring error from Tiernan Brooks, as Joe Stacey’s cross was misjudged by the ‘keeper.
But the Tigers equalised from the penalty spot just minutes later through Steven McDonnell.
Worksop controlled the second half but failed to get ahead, which led to Frickley countering one of those attacks to score at the death to win the derby.
Parry said: “I am still struggling to think how we have lost the game.
“I don’t mean that we were totally the better side; what I am saying is that they have had one shot in the second half, and it was horrendous defending from us because we have enough experience in that backline that should stop that goal.
“We’ve had a couple of snapshots around the area and there were some chances there that we should have score and if we had, I believe we would have gone on and won the game comfortably.
“But, again, we didn’t take the chances and we didn’t have the quality in the final third to create more clear-cut chances.
“When you don’t do that, you’re left open to counters as we saw there with one straight ball – I cannot tell you how frustrated and disappointed I am with the goal.”
Worksop welcome Newport Pagnell Town on Saturday in the FA Cup.
The Swans have had a superb start to the season, scoring 24 goals over five straight victories but they have had their last two games postponed due to positive covid cases.
“I think we need to get in on Thursday before the FA Cup and readdress a couple of things,” added Parry. “I think we need to go back to basics a little bit.
“We have done a little background check on them with a few teams from their division and they are a very strong side.
“They shouldn’t be operating at the level they’re at and they have some really good players in there attacking-wise, so we must be on our guard and try and have them on the back foot.
“It will be an extremely tough game because the expectations are on us but sometimes the levels of the leagues don’t bring a true picture, and this is one of those games.”