A haul of 13 points from a five-game run that began on the final Saturday in March means the Minstermen are now guaranteed another season in the Football League.
It has been the third consecutive season that York have finished strongly in League Two, taking 14 points from a possible 18 in 2012-13 and 13 from 21 last term.
“The emotion is probably relief,” admitted Wilcox ahead of today’s trip to Shrewsbury Town.
“It has been a big weight to carry. The drop from League Two to non-league is huge.
“It affects a lot of people at the club. You don’t get Academy funding, for instance. The pressure has been there to make sure it didn’t happen. So it is a relief to have come through that.
“It is like a big black cloud has moved on and now the sun is shining.”
Wilcox’s first game was at home to Shrewsbury, a 1-0 defeat dropping York into the relegation zone in October.
He added: “We can look up now. I would say there are three or four teams that we can try to get past and that would put us mid-table.
“It is important to finish the season well and it gives everyone hope for next season.
“If we can get a couple more results then people go away in a better frame of mind. Hopefully, that will carry on into next season.
“I was always confident but you never know in sport. We did drop into the bottom two briefly. But getting out so quickly was huge.
“To me, that was vital. It meant more pressure was on others, those in the bottom two. In any division, there is no team that is too big to go down. Look at Bristol Rovers last season.”