Buckingham said it “really grated” him at the time that he had not been able to show people what he could do as a coach, particularly because of working in his home city.
A strong run of form in the final 10 games rescued a play-off spot for Oxford before a semi-final victory over Peterborough United en-route to going up.
“The pleasing thing was kind of how it all played out,” Buckingham said.
“To finish the season the way we did, to enjoy that day and the way we played at Wembley was arguably the best game of football I’ve ever stood on the sideline and coached.
“And to be able to do that in front of 35,000 Oxford fans and to do that on a stage in front of the rest of the country, it was a nice moment.
“That moment when the referee blew the full-time whistle… I can’t quite describe the feeling I had. There are no words. That’s probably the most special thing for me, you can’t describe it.”
Oxford are currently ninth in the Championship with three wins from their first six games and host Burnley on Saturday.