An injury-time goal from Tom Watson earned Sunderland a 2-1 win and promotion at Wembley.
A shell-shocked Wilder said afterwards: "It's going to take quite a while to get over, for the players, the staff and most importantly the supporters.
"Congratulations to Sunderland, the manager and the players for the achievements this season and going into the Premier League.
"It's a tough one to take from our point of view. Defining moments in the game I get. We never really felt in danger even sort of second half. Of course they've got to open up and try and get back into the game we just needed to be better on that turnover."
Second-half criticism
Wilder also said, "I think the biggest thing for us was we were too loose second half. We have that ability to sit in. They're piling people forward and then we go and kill them on the counter attack and we never found that moment, we were loose.
"It was disappointing to concede the second goal in the 97th minute, I know we were down to 10-men but it goes up to the centre-forward and it's loose again and they find the two moments.
"Everyone talks about stats, I think we had the biggest chances but stats doesn't win you the game. They found their moments and we haven't found our moments. They find themselves in the Premier League and we've got to go again."