The Bantams controlled much of the game and took the lead through Garry Thompson just before the hour after an error from Dons defender Alan Bennett.
But with the match approaching its conclusion, substitute Jack Midson equalised in the 83rd minute, before Alexander headed in a Toby Ajala corner in the third minute of stoppage time.
"I don't think it showed in the way we played that we had Wembley on our minds. I couldn't fault the lads," said Parkinson.
"Being beaten in the manner we have done is very difficult to take. It's going to take a while on the way back to get this one out of my system. We deserved three points rather than one so to come away with nothing is unbelievable.
"We've got a great week ahead of us, the lads deserve it, they've worked exceptionally hard to get to this stage and we're going to enjoy it.
"I don't want to change things too much, we'll prepare as professionally as we can for Swansea. They're an outstanding team who control games against Premiership opposition, but we'll go there, have a real go and do the club proud."
"If you look at all the teams that have had big cup wins like MK Dons and Luton, they've struggled in the league, so it's naturally going to affect you. But I've been pleased with all of our performances since we reached the final.
"It's going to be on your mind because everyone's talking about it. but it will be a great day for the city of Bradford and we're going to enjoy it."
- Sports & Recreation
- Jack Midson