The Minstermen had been embroiled in a relegation scrap for the duration of the campaign but a 2-1 home victory over Morecambe extended their well-timed unbeaten run to a sixth game.
It also ended the Shrimps’ outside hopes of gatecrashing the play-offs.
Skipper Russell Penn won the match on 51 minutes with an thunderous 35-yard strike after his team-mate Stephane Zubar had headed in a Luke Summerfield corner to cancel out Paul Mullin’s opening goal for the visitors.
A delighted Wilcox said: “It’s been a tough season so to get over the line with three games left to play is an outstanding achievement from everybody and a big weight off everybody’s shoulders.
“The important thing is we have done it ourselves and not had to rely on other teams.
“We have gone on a terrific run at the right time with four wins and two draws in six games, which has seen us home and dry. Now I want to carry that on in our last three games to take some impetus into next season.”
Wilcox was unhappy with his team’s start to the match with Mullin pouncing from six yards to net after 10 minutes but was left purring following a second-half display that was capped by his captain’s goal-of-the-season contender.
The York chief added: “We were awful for the first 10 minutes and gave the ball away to them so many times. We looked nervous and the atmosphere was a bit flat but maybe them scoring gave us the jolt we needed because the second-half performance was outstanding.
“Russ’ goal was incredible. I won’t say it’s a once-in-a-career strike but it could be.
“He was 35 yards out and it flew into the top corner. There’s probably not been a better goal all season.
“We’ve already been putting a DVD together of the best ones for the presentation night but he might just have pinched that award now and I’m pleased for Russ because, as captain of the club, he has carried a lot of the weight on his shoulders. He has to lead the club and he’s done that superbly.”
Morecambe boss Jim Bentley, meanwhile, bemoaned his team’s failure to take their top-seven push into the final weeks of the campaign, citing Zubar’s 34th-minute equaliser as the turning point.
He said: “I’m frustrated because we could have had the game wrapped up in the first half-hour. We were excellent and cut them open.
“We got the goal and also looked dangerous at set-plays but they got the equaliser which I thought might have been a foul and then we lost Ryan Edwards to injury and had to switch to 4-4-2.
“They then came back into the game but they must have gone in at half-time amazed it was 1-1.”