Crewe were left heartbroken after dominating only to slip to defeat thanks to Wilson's brace.
The win leaves Coventry all but safe in League One, but Crewe are still deep in a relegation battle after winning just once in eight games.
"When you've got Callum Wilson, you've always got a chance, with two great goals from him," Pressley said.
"We didn't play with our normal passing fluency, but the one thing we gave was guts and heart and we've done that in the last two games.
"I'm really proud of the players for that, because I don't think this season, until Wednesday night, we'd won ugly - and we have won ugly and we've shown people we can win ugly.
"I said at the start of the season, if we were to escape relegation, when you consider everything we've had to endure, I think that would be a massive achievement.
"Because of the circumstances and the 10-point deduction, we've found ourselves in a difficult predicament.
"If we look at the league table, we'd actually be level sixth. That's a hard pill to swallow."
The first half saw relatively few chances created, but Crewe had two early let-offs as Wilson first fired off target before a clearance hit City's Anton Robinson on the head and rebounded just wide of goal.
Alex pair Uche Ikpeazu and Mark Ellis then fired off target for the hosts as they looked for an equaliser.
Moments later Crewe went behind as Wilson grabbed his first of the game.
There was a slice of luck in the goal as the striker found himself in exactly the right place when Franck Moussa's surging run ended in a shot that rebounded off the post.
But Wilson was also quickest to react, sticking out a right leg to direct the ball into an empty net.
The goal livened the Gresty Road crowd up and the home fans were left furious just before half-time when a clear shirt pull on Ikpeazu in the box went unpunished, with the striker eventually wriggling clear and shooting across goal.
The home side then dominated the second half and after Ikpeazu had missed two good chances they finally made the breakthrough, equalising with an own goal.
Coventry had had a scare seconds earlier when Andrew Webster deflected a pass just round the post, and from the resulting corner Joe Murphy failed to deal with the ball into the box and Jordan Clarke put the ball into his own net.
Alex pushed hard for a winner, with Matt Tootle forcing a great save and Ellis coming close.
But they were stunned on the counter-attack as Carl Baker found Wilson with an excellent through ball, and the striker duly netted a superb second.