The Hoops beat Frank de Boer's Amsterdam outfit 2-1 with goals from James Forrest and Beram Kayal to claim their first Group H win.
But left-back Blind - son of Ajax's former European Cup-winning captain Danny - says the Dutch side should have left Celtic Park with at least a point.
He said: "We played a lot of moments of good football and came out to create chances. But Celtic scored two goals that were not really deserved at that moment in the game.
"They are a physical team and we had a little bit of a problem with that. But if you look at the chances, I think for sure we deserved one point here."
Ajax hit the post through former Liverpool midfielder Christian Poulsen in the first half while Thulani Serero missed two great opportunities after the break before Lasse Schone eventually found the net in time added on.
That left Blind to admit: "Maybe if we had taken our chances we might have even won."
Blind was up against an on-form Forrest, who shook off the effects of a virus to score with an emphatic penalty in first-half stoppage time.
But the Holland international denied his opponent had the better of him.
"He is a good player, a young talent," said Blind.
"He is really fast but a couple of moments I had him and one or two moments he had me. It was a good game."
The defeat leaves Ajax - who host the return clash with Celtic at the Amsterdam ArenA on November 6 - bottom of the group with just one point from three games and Blind admits his side are now realistically only targeting a Europa League slot.
"We need to win in Amsterdam if we want to play for the third place," he said.
"We know that and I look forward to it. As for second place, maybe we can look at that if we beat Celtic."