Devlin was first booked by referee John Beaton for a challenge on Papa Gueye in the 76th minute, with Hearts head coach Neil Crichley disputing that decision as it came after the Aberdeen striker had been flagged offside.
The Australia midfielder, 26, was then shown a second yellow, with Critchley saying Devlin would not have seen Dante Polvara arriving late as he tried to clear just outside the penalty box.
“It is the club’s view that neither yellow card issued to Cammy Devlin in the match was warranted and we should not have been put in the position of having to finish the game with nine men, which directly affected the outcome,” Hearts say.
“Saturday came on the back of other decisions this season that have also not gone in our favour.
“Once again, we will engage with the Scottish FA in an attempt to understand why these decisions are made, see acknowledgement as to when they are indeed wrong and determine what can be done to learn from them to ensure that they are not repeated.”
Hearts say they have “maintained dialogue” with the governing body throughout the season on such matters and “prefer to air our grievances in private”.
However, on this occasion, “given the magnitude of the occasion and what was at stake”, they thought they should make it clear to their supporters that “public silence on our part should not be mistaken for inaction”.
They added: “To have nearly 22,000 Jambos inside Hampden Park was an incredible feat and your support undoubtedly inspired the team on the pitch to battle until the very end, where, against all odds, it looked as if the players had earned the opportunity to take the match to penalty kicks, and deservedly so.”
Hearts, who sit seventh in the Scottish Premiership, must now steer clear of relegation trouble in their remaining five games in the bottom six.
“The club has recently publicly declared that this season has not been good enough and it is our intention not to see it repeated,” they added.
