Already carrying a booking for a crunching first-half tackle on Liam Boyce, the defender picked up a second caution for hauling down Cammy Devlin on the edge of the box in the last play of the game.
St Mirren will now be without their captain for Wednesday's visit of Ross County and are already without the services of Conor McCarthy, who is facing up to four months on the sidelines with an ankle injury.
Goodwin believes Muir could have handled Shaughnessy's foul a lot differently.
He said: "I was disappointed. I can see why Alan Muir's come to that decision.
"Joe was last man and there is a bit of grappling on the edge of the box and you could argue if the Hearts player gets away then he has a free hit at goal.
"But in the 95th minute when Hearts are 2-0 up and the game is done, I don't think anybody would have minded if the referee had turned a blind eye to that one.
"Unfortunately, it's a big call for us because we are missing Conor McCarthy already with a lengthy injury and we're going to have to go without Joe for a game now as well."
St Mirren put a lot into the clash on Saturday and could easily have left with all the spoils had they taken their chances.
Gary Mackay-Steven put the hosts in front with a 61st-minute finish from close range before Stephen Kingsley wrapped up the points with a stunning free-kick from 25 yards in the 75th minute.
Goodwin added: "It would be a lot easier for me to take if I felt Hearts had completely dominated the game.
"Then you hold your hands up and say the better team won, but I genuinely feel a draw would have been fair over the scheme of things.
"We have to dust ourselves down because we have a tough run coming up.
"We have to get back to winning ways and we have to do it soon."
Saints host the cinch Premiership bottom side Ross County in midweek, followed by Hibs, Celtic and Rangers.