Reading needed to win at the Madejski Stadium to keep their survival hopes alive, but the result condemned both clubs to the drop from the Premier League.
Adkins, who only took charge of the Royals in late March, was disappointed to suffer relegation and is demanding a positive response from his squad.
"I said to the players in the dressing room that it's not nice getting relegated and I never want to be in that situation again," Adkins told Sky Sports. "We've got to bottle that feeling.
"We've got another game coming up next weekend against Fulham and two more games after that. We've got to put ourselves in a situation to keep progressing as a football club.
"We're going to be a Championship football team so what we've got to do is give ourselves an opportunity to get back in the Premier League and learn the lessons quickly from this season so we're in a position to be equipped to get back in the Premier League and to give ourselves the opportunity to finish higher than we have done this year."
Asked if there were things he would have done differently since taking charge, Adkins replied: "When you look at it, there's been a good progression.
"We want to play winning football. Today both teams came out with different ways to win a game of football, but unfortunately it's ended up with a 0-0 scoreline which didn't help anybody.
"We've got a nice bunch of lads who work hard. It's a great football club and we have to rebuild and get ready for next season.
"There is an opportunity to do that already and the mindset is we're looking forward to next season. The lessons we've learned from this season are invaluable."