The stuttering Jambos conceded a penalty midway through the first half when Andy Webster felled James Drayton - and Liam Kelly made no mistake from the spot.
Thereafter, McGlynn's visitors failed to force an equaliser despite creating chances and were left to ponder what might have been as they missed the opportunity to go level on points with city rivals Hibernian.
McGlynn said after seeing his side drop to ninth in the table: "There is nothing in any SPL game.
"Every game is very close, our 2-1 win against Dundee United at the weekend was very close as well but it is goals that win you games and we did everything today bar get the ball in the back of the net.
"We have been scoring goals recently so I can't mump and moan too much. It was a good performance from the players and they had a good attitude.
"I thought they worked extremely hard and did everything bar score, I couldn't ask them for much more.
"I thought we dominated the second-half, we had plenty of chances but the ball didn't fall kindly enough for us to get a good clean connection on it in front of goal."