Captain James Cook was shown a straight red card two minutes before half time for a tackle the referee deemed reckless and although opponents Leicester City were reduced in numbers when they had a player sent off four minutes from the end of normal time, Boro's players had still put in an extra shift.
The only goal of the game came a minute before the end of the first half of extra-time when a 20-yard shot took a wicked deflection.
"It was a cruel way to go out," says Mark Tinkler. "I can't fault the effort of the players, you can only do your best.
"The sending-off didn't help. I know James is a whole-hearted, committed player, but he's not a dirty one and he would never intentionally go over the top.
"I made a substitution and we re-shaped, but we didn't sit back, we tried to make them play through us and took the game to them as often as we could, at times it didn't look as though we had ten men."
Boro hit the post and had one cleared off before the deflected effort on 104 minutes ended their interest in this year's contest.
"Players have to learn how to cope with the heartbreak of situations like this if they are to go on and have a future in the game," says Tinkler, a talented and experienced player himself.
"I hope they're hurting and I think they are, it shows they care."
READ: Match Report