Stark originally named a squad of 18 for Wednesday's friendly in Korinthos but was hit by call-offs ahead of the trip.
Fraser Fyvie, Stefan Scougall, David Smith and Lewis Toshney were all forced to withdraw through injury, with late call-ups for Fraser Kerr and Callum Tapping.
Stark said: "We are a wee bit tight with numbers but it depends where you are in the building process. We've had the game in Portugal and we had a couple of games in Malaga.
"We're at the stage now, going into a championship game, that I wouldn't want to have a whole big squad of players to try to fit in. You want players to get plenty of game-time to see how they look."
He added: "We knew about Fraser Fyvie, after he pulled his hamstring in the FA Cup tie last week so we were always doubtful that he would make it. He was pushing to try to be here but couldn't make it.
"I saw Stefan getting the injury on Saturday and I saw David Smith getting the hamstring injury on Sunday so I knew right away.
"Lewis Toshney has a knock and we don't want to risk him.
"We are quite comfortable with the ones we've got. We're excited for Stuart Bannigan, Stephen O'Donnell and Callum Tapping to get an opportunity. Rory McKenzie is another new one.
"It means when we go into the championship game in six week's time, we've blooded another couple of players that, if needed, are there for us."