The Hammers were reduced to ten men 19 minutes into the biggest game in the club's recent history after a sloppy challenge from the Englishman.
Trailing 2-1 on aggregate after the first leg of their Europa League semi final, David Moyes' side saw the difficulty of their task increase when Cresswell pulled Jens Petter Hauge down with the Frankfurt forward racing through on goal.
Referee Jesus Gil Manzano initially gave the West Ham defender a yellow card, but upgraded the punishment to red following a VAR review, with Cresswell adjudged to be denying a clear goalscoring opportunity.
The 32-year-old was also sent off for a similar offence in the first leg of West Ham's quarter-final triumph over Lyon.
Despite Cresswell's protestations, Ashton insists he only has himself to blame, having misjudged the one-on-one situation caused by a long ball forward.
Aston told talkSPORT: "Ultimately, I can't see why it isn't [a red]. It has to be. I don't know why he's trying to win it, he just needs to drop off.
"He doesn't win it and he's climbing all over the opponent.
"Cresswell can have no complaints, it's his own fault, he just needs to shepherd him.
"You certainly don't plan for that. I don't know what he was thinking.
"You know what it was? It looked like panic. He was so desperate, the striker had the pace on him.
"He missed the ball completely and it was a clear red card. I couldn't believe the ref gave a yellow.
"I'm sure he's distraught inside the dressing room. There's no way he meant it, but he can't take it back. He has to hope West Ham can do something special."
Aston added: "It's better the striker scores than Cresswell gets sent off. But this atmosphere, this pressure, it forces decisions and he made the wrong one."