United lost 3-2 to Luton Town after extra-time in London, with Adkins feeling that all three goals conceded were preventable.
The winning goal five minutes into extra-time, in particular, was a result of a horrible mix-up between the left-back Marcus Williams and goalkeeper Joe Murphy.
"The story of our season has been giving away poor goals, and we gave away three," said Adkins.
Adkins: Next time we'll win
"We have not performed to the levels we would have liked to have done. Credit to Luton, I congratulate Mick Harford and his team, but we have to learn from this negative experience and use it in a positive way.
"I made sure they will remember this because it's not nice. There are a few tears becaause we have lost a cup final.
"It's disappointing but we've got a very young group of players and they will learn about themselves. We've got to utilise this experience now.
"We will draw a line under it and make sure we come back to Wembley in the play-off final. And make sure we win."
The League One play-off final will be held at Wembley on Saturday May 24.
Scunthorpe are sixth in the table, occupying the final play-off position, with two games in hand on the two teams immediately below them.