Dougie Hill was sent off by referee Brian Colvin in the 74th minute for an apparent head-butt that left Jamie Hamill grounded but Murray watched television footage of the flash-point, which came when the teams were tied at 1-1, and insists there was no contact.
Both goals came after the break with Hamill cancelling out Liam Fox's opener. Brad McKay scored the decisive penalty as Hearts won 5-4 from the spot.
"It was not a sending off, I've seen the video evidence just now," Murray said.
"It changes the game as well. We have to take it on the chin and move on.
"I've not spoken to the ref, I've just watched the video. Dougie is saying he never touched him, he is saying they walked up to each other and the Hearts player went down.
"It's very disappointing. You see it in a lot of games with players going together, if there is no contact there it's very disappointing from our point of view."
Hearts manager Gary Locke hailed his side's character after they came through on penalties.
"It was certainly not what we wanted with it going to extra-time," Locke said.
"We did not do too well in well in the first half but the second half was a lot better. They got everyone behind the ball when they went down to 10 men.
"We're delighted to be through, the boys' character was fantastic."