Talismanic striker Mullin needed oxygen after goalkeeper Nathan Bishop clattered into him during a friendly against Manchester United in the United States on Tuesday.
The Red Dragons won the match 3-1 but Mullin was diagnosed with a punctured lung after a surprisingly ill-tempered game.
United midfielder Daniel Gore was shown a straight red card for a separate tackle, but Wrexham captain Tozer was reluctant to blame Bishop for the challenge which punctured Mullin's lung.
Tozer did, however, reveal that Mullin is unable to fly home from the States with just ten days until the start of the League Two season.
"The red card was pretty poor," the defender told talkSPORT.
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"There were a couple of bad challenges. The one from the keeper was probably not that bad but it resulted in a bad injury.
"There were a couple of tasty challenges to say the least."
On Mullin, Tozer added: "I'd say he misses the start of the season, definitely. I believe he's punctured his lung. I don't think he's able to fly and it's going to be a big loss for us.
"He'll come back with the bit between his teeth. We'll miss him but we've got players of real quality who can step in."
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Manager Parkison, however, was far less diplomatic when asked about the challenge from Bishop.
Parkinson said: "I'm fuming about it, I've got to be honest with you. It was a clumsy, reckless, challenge in a pre-season game and I'm not happy with it at all.
"I haven't seen the goalie and he's probably best steering clear of us for the time being because we're not very happy.
"It should have been a straight red. If it's not denying a goal scoring opportunity it's still a dangerous challenge so if you add the two scenarios together he should have been off the pitch.
"It's a dangerous challenge and obviously Mullin is our talisman. The way the lads responded after that I thought was outstanding. That's what we're all about as a group - resilience, sticking together."