Wright's Saints went marching on at Stark's Park on Saturday when they beat Championship side Raith Rovers 3-1.
Back in early February, St Johnstone were hammered 4-0 by Aberdeen in the semi-final of the League Cup.
And Wright said: "I have said to the players that we deserve another crack at a semi-final to lay the ghost of the Tynecastle result.
"Hopefully, we can also get a crack at a final. If we play the way we can play I don't think it matters who we play in the semi-final, they are all about who plays on the day.
"But to go there and play badly and win would be perfect."
On a windy day in Fife, Gary McDonald fired an early opener, before Rovers midfielder Joe Cardle levelled matters on 21 minutes from 30 yards.
Nigel Hasselbaink restored the Scottish Premiership side's lead from close range in the 49th minute, while Steven Anderson completed the scoring on 78.
Wright added: "Conditions played a big part in the game. Alan Mannus had a kick out which didn't even reach the centre circle.
"We made some individual errors which were probably down to conditions.
"But it was strange, the flags were going one way and the wind seemed to be going the other. It probably made for an exciting cup-tie.
"They got a goal out of the blue with a tremendous strike and had two free headers so we were happy enough to come in at 1-1.
"We played really well in the second half and no one can argue that we didn't deserve the win."