Neil Lennon guided his Hoops through to the Round of 16 with a 2-1 home win over Spartak Moscow to finish second in Group G behind Barcelona and McGlynn feels it is a great achievement for the Glasgow club and Scottish football in general.
"You've got to give a lot of credit to Neil Lennon and his players; fantastic achievement," said the Jambos boss.
"They've come through a lot and it's great for Scottish football. It helps the co-efficient and it can only be good for Scottish football.
"We take enough knocks. I think we should be trying to pat ourselves on the back in some form that one of the SPL clubs have managed to achieve to get to the last 16 of the Champions League."
"I'm delighted that they've made it and hopefully the country will get behind them," he said.
"We should be accommodating our European representatives a bit more. Celtic played last night and they have to play at lunchtime on Saturday. I don't think that's fair.
"It puts a bit of an advantage our way."