United won the penalty shootout 4-3 after a 1-1 draw in normal time. Adkins did not name any first-team regulars in the squad.
"After scoring a very good goal through Adam Boyes early on, a very young side had to hang on," said Adkins.
"Niall Canavan, who has just come back from injury, was top drawer alongside youth trainee Ashley Palmer at centre-back.
"From that point of view it was a good lesson to stay in the game and win the competition."
Trialist right-back Trent McClenahan played the full 90 minutes after a week training with the first-team squad. He has international experience with Australia at U23 level and turned down an offer to stay with Scottish Premier League side Hamilton Academical this summer in a bid to earn a return to England.
"He's very composed on the football. He has good experience and has played at a higher level," added Adkins.