Rangers defender Bilel Mohsni received a second yellow card after his team's 1-0 victory on Thursday after remonstrating with Airdrie manager Gary Bollan as both teams left the field.
Mohsni had earlier been booked following an off-the-ball incident with Airdrie striker Jim Lister and he reacted angrily to several other challenges during the game at the Excelsior Stadium.
Rangers midfielder Ian Black was also booked for pushing an opponent following a bad tackle and Airdrie had a total of five players booked.
Clark, who won the division last season with Queen of the South, said: "Teams are going to come and be physical against us. They want to beat us. But we are ready for each game and if they want to be physical like that then we will match it."
Mohsni has incurred an immediate one-match ban and will miss Sunday's rearranged visit to Stenhousemuir.
But Clark could understand why he reacted the way he did.
"Big Bilel knows what it's all about, but it's hard not to react when people are in your face and pushing you about," he said.
"That's just what he's all about. It's great to have himn in the team. He doesn't like getting messed about, and I don't think anyone would mess him about to be honest.
"It's a bit unfortunate he is suspended. He is a big player for us, but I'm sure whoever comes in will do well and we will be fine."
Runaway leaders Rangers had to hang on for the victory against the bottom club despite opening the scoring through Lewis MacLeod in the 18th minute.
Their own chances dried up early in the second half and goalkeeper Cammy Bell saved their 100 per cent away record in the league when he got down brilliantly to stop a Willie McLaren shot in the closing stages.
"We know it's going to be hard when we come away," Clark said. "Airdrie upped their game a lot. If they played like that every week I don't think they would be where they are.
"But fair play to them, they made it really hard for us. They defended well and they attacked us well at times but we got the goal and we took the three points."