The Dragons jumped five places to 10th thanks to Nathan Broadhead’s early strike and a late own goal at SToK Cae Ras, continuing a surge that has brought four straight home victories and a seven-game unbeaten run.
The result leaves them only two points outside the play-offs – but Parkinson insists the ambition within the club goes well beyond their current position.
“I’d rather be where we are than any lower, but I would still like to be higher,” he said, making clear that the club’s remarkable rise through the divisions has not dulled expectations.
While supporters may already be whispering about another promotion challenge, Parkinson stressed that Wrexham must keep their focus tight and their feet firmly planted.
“It’s a good night but I think we’ve to be really careful we don’t get carried away with it,” he said.
“But we won’t, and we’ll be ready to put in a good performance at the weekend.”
READ MORE: Wrexham Ready to Unleash Kieffer Moore on Tractor Boys
Wrexham set the tone early, with Broadhead’s brilliant 16th-minute finish breaking the deadlock.
The summer signing has struggled to find consistent scoring form since his switch from Ipswich, but his third league goal in red sent Wrexham on their way.
Bristol City threatened at times – including a Ross McCrorie strike disallowed before the break – but the hosts remained the more purposeful and better-balanced side throughout the contest.
The victory was sealed when George Thomason’s dangerous corner struck the upright and deflected into the net off visiting goalkeeper Radek Vitek.
READ MORE: Give Me Moore! . . . Any Team in the Championship Would Love In-Form Wrexham Striker
Reflecting on the performance, Parkinson said: “It was an excellent win. I thought the first 35 minutes was really good and we were rewarded with an excellent goal from Nathan.
“They came into it, which you’d expect. They’re a good side and they had moments but we had some great chances ourselves.
“We’ve really taken the game away from them. We got back to that quality with possession and the work without the ball remained.
“But all in all, I thought we built from the weekend. We spoke to the lads after the Ipswich game about having a really good structure, work ethic and team togetherness.
“But it was about if we could now get back to that quality in possession ourselves, and I thought we did that tonight.”
READ MORE: Phil Parkinson Hits Back at Critics As Wrexham Prove Their Championship Worth
The win extends an impressive run that has fuelled talk of a top-six push.
But Parkinson was told his players they have to keep their eye on what is immediately in front of them and the things they need to do in order to win the next game.
“We’re just working towards the process of performance levels on a game-to-game basis, adapting the team, the shape, and the personnel within that to give ourselves the best chance of getting results,” he said.
For City, manager Gerhard Struber was left frustrated by the manner of the defeat.
“I’m really frustrated how cheaply we lost this game,” he said. “The first goal was really cheap… a little bit sleepy. Not the typical face from us.
“When we have so many good moments we should to score a goal but we were not sharp enough.”
For Wrexham, though, the night reinforced their fans’ growing ambition of finding a way to the Premier League from their first season back at this level.
