The Welshman, who won the club’s Player of the Year award last month, is eager to learn from the Wembley heartbreak and hailed the support over the past season.
He wrote on social media: “Saturday hurts, sorry we couldn’t finish the job and achieve what we all wanted, time to reflect and grow from it, thank you for your support throughout the whole season.
Sheehan has been a key figure for the Whites in the middle of the pitch since the start of the campaign, getting 12 assists in the league.
The 29-year-old was also nominated for the PFA League One Fans’ Player of the Year Award last week due to his consistent performances.
However, he failed to make his mark against Des Buckingham’s side and was taken off as part of a triple change on 65 minutes.
Jack Iredale also apologised for the lacklustre display against the U’s, who clinched the final spot in the Championship next season.
The defender came off the bench for the final 25 minutes as part of a tactical shake-up that saw Josh Dacres-Cogley move to the left of the back five.
Iredale was crushed by how the afternoon panned out on the big stage but vowed to come back “bigger and stronger”.
He added: “Words can’t change the past. That’s going to hurt for a long, long time. Can only apologise to the fans for letting you down on the big day. Will be back bigger and stronger from this.”
Aaron Collins shared a heartfelt message of his own earlier this afternoon, apologising for the performance and vowing to “do everything” to put things right next season.