Reading were on course to qualify for the Championship's playoffs until Brighton & Hove Albion struck a last-gasp winner at Nottingham Forest to edge ahead of the Royals, who could only draw with Burnley.
That left Reading seventh and an agonising point shy of the top six.
"I said to the players after the game that they should bottle up the horrible feeling," Adkins told the club's official website.
"I've experienced euphoria in my career but you also need to feel the hurt so it galvanises you and gives you the perseverance to keep going when things go against you."
Reading would have in fact finished fifth if they had scored a winner against Burnley as Wigan Athletic fell to defeat at Blackburn Rovers.