Saints reached the final four last season but were eliminated by eventual winners Leicester City.
"We played against Leicester and they won the FA Cup, so we lost against the winners," Hasenhuttl told reporters.
"It's a pity, maybe more was possible.
"To come in the semi-final maybe it was a big success and this is what we want to reach again. The semi-final must be our target, or even more if it's possible.
"One time at Wembley you want to go to the final and have a chance to win."
He added: "It's getting tougher every year because the top teams are getting stronger and are taking it more seriously.
"We have to take it round-by-round. Coventry won't be an easy game; it will be a tough challenge."
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