The scores were level at 0-0 when Dicker saw red for a challenge on Jambos’ winger Callumn Morrison, with the visitors scoring 10 minutes later.
Referee Willie Collum raced over to the incident and wasted no time in reaching for his back pocket, reducing the hosts to 10 men for the remainder of the match.
“Gary won the ball, clearly”, said Clarke after reviewing the incident post match. “We’ll win the appeal so that’ll help us next week, but not today.
“The most disappointing thing is that such an experienced official couldn’t wait to get the card out of his pocket, rather than taking his time and assessing the situation.
“It wasn’t (Uche) Ikpeazu that won the game for Hearts. It was the referee, unfortunately.”
Asked whether he’d sought an explanation from Collum after the match, Clarke replied: “No, I don’t bother speaking to referees after the match. It’s just not worth it.”
Meanwhile, Hearts manager Craig Levein praised his side for showing the quality needed to win following the red card.
Summer signing Uche Ikpeazu netted the winner with a deft header from the edge of the box, in what was his fourth goal for the club since making the switch from Cambridge.
Levein was full of praise for the centre-forward.
“Uche is still a really young guy”, the former Scotland boss said. “He’s just moved up here to a new country and he doesn’t really know the league yet. He’s been on a bit of a goal drought lately so it’s great to see him back on the scoresheet.
“I actually got more worried when Killie went down to 10 men. They’re really compact and well organised as it is and I thought it would be an even tougher task to try and break them down when they had 10 men.
“I was worried we wouldn’t be able to find the quality to get the goal but all credit to the boys who kept plugging away. We had a few chances and eventually we got there.
“We dominated the match before the man got sent off so I’m just really pleased we managed to get the win that our play deserved.”