The William Hill Scottish Cup holders gave themselves the rare chance of a back-to-back cup final victories with a semi-final penalty shoot-out win over Inverness at Easter Road on Saturday.
The Jambos will play St Mirren, who pulled off a shock 3-2 win over Celtic on Sunday, in the final at Hampden on March 17.
However, McGlynn wants his players to get ready for a side who, despite being bottom of the SPL, have already beaten the Gorgie men twice this season.
"It will have been a wee while, if anyone at all outside the Old Firm, has done back-to-back cup wins, Scottish Cup and League Cup, so it would be an achievement but that is as far as I would go with it," he said.
"We don't want to get carried away.
"Bradford are in the League Cup final in England and there were a lot of shocks at the weekend.
"Everyone had Celtic as big favourites so I am probably as surprised as everyone else but St Mirren played exceptionally well.
"But the final is March 17, a million miles away and we have so many league games to play between now and then, so the League Cup final goes on the back burner.
"Wednesday night is the priority for me, it is really important because Dundee have beaten us twice and we have had two sore lessons."
- Sports & Recreation
- League Cup
- St Mirren