The Pools took a two goal lead in the first-half but were pegged back in the sixth minute of added time in the second-half, leaving the game to go to extra-time, where they eventually lost 4-3.
Bates admitted the result was a bitter pill to swallow after showing so much passion.
“I’m not going to make excuses, blame the referee or be unprofessional about it but it’s a real hard one to take because the lads were fantastic," he told the club's official video service.
“It's hard to take but they’ve done everything we’ve asked, the gameplan worked up until the very last minute and I couldn’t be more proud of them.
“As coaches and players, we can’t legislate for Carl putting his hand up, I don’t think he can and he knows he made a mistake but it happens in football and it happened at the wrong time for us.
“But I can’t fault the lads’ effort, work rate or the way they applied themselves and they should be proud of themselves.
“If they keep doing what they’re doing, playing like that, sticking to the gameplan and playing with that desire and determination then we’ll get results sooner rather than later.”