The Wrexham manager conceded it was “two points dropped” after a late equaliser denied his side a fifth successive away victory.
The Dragons were seconds away from moving into the Championship play-off places before Max Bird’s stunning 89th-minute volley rescued the hosts at Ashton Gate.
Instead of climbing into the top six, Wrexham left sitting seventh, level on points with Derby but outside the promotion spots on goal difference.
For Parkinson, the frustration centred on a first-half display he rated among his side’s best of the campaign.
“It’s as good as we have played, we had complete control. We were patient and we got a goal with a brilliant finish from Ollie,” he said.
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Ollie Rathbone’s instinctive strike after 34 minutes – his sixth goal in all competitions this season – capped a dominant opening period.
Wrexham gradually tightened their grip after a cagey start, with Callum Doyle going close before Rathbone lashed home from 10 yards after a deflected cross dropped kindly in his path.
Parkinson felt his team executed their game plan superbly before the interval.
“We’re never going to dominate the second half like we did in the first, it doesn’t work like that in football.
“It does feel like two points dropped and of course, the dressing room is a bit quiet.
“But as a manager I’ve got to stay calm and collected because the lads have given us a lot to like.”
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Bristol City were markedly improved after the restart.
Head coach Gerhard Struber reacted decisively at half-time, introducing Sinclair Armstrong, Delano Burgzorg and Jason Knight in a triple change that immediately altered the tempo.
“Our first half was really bad, too passive. It was not the football I want,” said Struber.
“We spoke at half-time about changing the behaviour. Think forward, play forward, and we bounced back.
“It speaks a lot about the boys that the reaction was good and we could change this result.”
City needed just two minutes of the second period to level. After Tomi Horvat forced Arthur Okonkwo into an early save, Armstrong rifled in from a tight angle to end his seven-game goal drought and swing the momentum.
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The contest opened up from there, with both sides carving out opportunities.
Nathan Broadhead and Armstrong threatened, while Parkinson reshuffled by introducing Kieffer Moore, Josh Windass and George Dobson for the closing stages.
Wrexham regained the advantage in the 76th minute, albeit fortuitously.
Issa Kabore’s driven cross was diverted into his own net by substitute Joe Williams, handing the visitors a 2-1 lead and seemingly putting them on course for another valuable away win.
Dobson then squandered a glorious chance to seal the points nine minutes from time, dragging wide after slick interplay between Windass and Moore had opened up the City defence. That miss proved costly.
With the clock ticking down, Knight’s delivery from the right was met on the edge of the area by Bird, who unleashed a ferocious volley that crashed in off the underside of the crossbar, leaving Okonkwo helpless and the home crowd in raptures.
Parkinson suggested the equaliser was a once-in-a-lifetime strike, insisting Bird would “never score a goal like that again,” but Struber was quick to defend his midfielder’s credentials.
“It’s not a coincidence that he scores a goal like that. Of course, you need a little bit of luck but he has the confidence in this moment,” Struber said.
“The message in this shot was a clear signal from him. I see it from training that he can score goals like that.
“It’s a good moment for Max and I’m really happy for him after five months out.
“We had special conversations in my office about his injury. I’m just happy he’s healthy and that he can help the team.”
Bird’s impact was all the more impressive given it was his first appearance in five months following a calf problem.
His intervention ensured City remain ninth, just a point behind Wrexham and firmly in the play-off conversation.
Wrexham, meanwhile, were left to rue missed opportunities.
Dobson thought he had a late chance to snatch victory deep into added time but steered Windass’ cross wide, although the offside flag had been raised.
For Parkinson, the overriding emotion was one of frustration rather than pride, despite acknowledging the quality his side showed.
Having controlled proceedings for long spells and twice led, the Dragons had positioned themselves perfectly.
But in a division where margins are razor-thin, a single lapse — or a moment of brilliance — can undo 88 minutes of hard work.
