Oxford could have sneaked into seventh place if they had won and Crewe had lost at home to Aldershot, but neither result materialised.
Wilder's men ended well beaten as goals by Marc Richards, his 17th of the season, Sean Rigg and substitute Ben Williamson secured a top-half finish for Vale despite a 10-point penalty for going into administration.
Wilder said: "Congratulations to Cheltenham and Crewe for making the play-offs and we can't have any complaints.
"We've had a decent enough season, but not winning a game in the last six weeks means we didn't deserve a place in there.
"Having said that, we are on an upward curve and this is the highest finish the club has achieved in 10 years. We can build again next season."
