The Dutch side were in a dominant position midway through the semi-final second leg, having won the first leg 1-0 in London and scored twice in the first 45 in Amsterdam, Ziyech hitting his club's second to seemingly send them on their way to the final.
But Lucas Moura's second-half hat-trick, including a winner in the sixth minute of stoppage time, left Ajax on the outside looking in as Spurs set a date with Liverpool in the final on June 1.
"This hits us hard, really hard," Ziyech told Veronica. "I don't know how it happened. I just don't know.
"We knew it would be very difficult if they scored after the 2-2, but we had chances.
"I could have scored, hit the post. At least one of my chances should have gone in.
"Then it would have been over, but then it struck us hard.
"I blame myself for this. We gave our all. The play wasn't great, but we kept fighting. Now disappointment prevails."
Defender Daley Blind was also left stunned, saying he didn't know what it would take for Ajax to come back from their stunning defeat.
"I don't know how to recover from this," he told Veronica. "I guess everyone has their own way, but we have to be back on track by Sunday.
"I'm glad we will be having another match soon. It hurts.
"Yesterday we've seen that everything is possible. We told ourselves that. We had a great opponent with lots of qualities. We delivered a lot of passion.
"After the 2-2 we restored the match. Hakim had two good opportunities. It's such a shame he couldn't finish it.
"This match should have lasted 10 less seconds. They didn't get many chances after the 2-2, but they scored anyway and that's devastating.
"I'm extremely proud to be part of this team. We've shown fantastic stuff and I think the whole world enjoyed it, but it's a bit too early for us to think like that.
"Anyway, we have to go on. We have to win another trophy with this team. We going to make sure the season ends in a fantastic way."
Manager Erik ten Hag also asked for his side to refocus quickly with the Eredivisie still up for grabs, but was not ready to discuss what went wrong for Ajax on Wednesday.
"We've played a great game, also in second half," he told Veronica. "We were almost there, so we're deeply disappointed.
"It's cruel. The players deserved to go to the final, but an unfortunate moment killed us.
"Now we have to recover because FC Utrecht is already waiting on Sunday.
"Now we can't think about that of course. Tomorrow we still can't, but we have to march on. For now, it doesn't matter what went wrong today."