Stark originally named a squad of 18 for Wednesday's friendly in Korinthos (kick-off 1pm GMT) 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."
The clash with Greece provides another opportunity to work with his players ahead of the qualifiers for the UEFA European Under-21 Championship for 2015 which get under way with the visit of Luxembourg next month.
Stark said: "We want to install a winning mentality so we are going to try to win the game but it's not the most important thing.
"You analyse the performance individually and collectively and, when you go into a championship game, hopefully you are a bit further on in terms of making judgements."
Asked what he can expect from the opposition on Wednesday, Stark said: "They are a big physical side.
"They have beaten Belgium 3-1 and they drew with Austria 1-1 so those are good results at international level, there is no doubt about that, particularly the Belgium one.
"We are expecting a tough game but hopefully we will have nicer conditions.
"That was the idea with the February friendly, to try to go somewhere where we could get good conditions to play.
"Hopefully that will be the case but we will be severely tested and it's going to be a good test for us."
The young Scots will face Holland, Slovakia, Georgia and Luxembourg in the qualifiers.
Stark said: "As with most draws, it could have been better and it could have been worse.
"We always approach it in terms of we've got a realistic chance of qualifying.
"We've taken it to the last game every time and we hope to do that again."