The Warriors moved up to second in the table and the former Scotland 7s star says the players not on international duty are gunning to keep their places as the league race hots up.
The Warriors have a short turnaround as they head off to Wales to take on Newport Gwent Dra-gons this Friday night.
McGuigan scored his first and second tries for the Warriors in his eighth run out for the Warriors this season.
"I drew the last man and just backed myself, got a good step on the defender. It helped because there was an option on the inside but there was still a little bit of work to do.
"The second was a little more straight-forward, but it was great team build up play and Ryan threw the big pass out wide, I just had to run in over the line but to get two scores and that monkey off my back was great.
"It's been pretty frustrating for me this season as I've been injured and not really had the chance to show what I can do, so to have started on Sunday and got two scores was great."
The first 10 minutes in Parma had the Warriors coaching staff exasperated with two cheap tries given away, but McGuigan says there was a quiet confidence among the squad that they could impose themselves on the game.
He said: "We knew that if we cut out the mistakes we'd be in with a very good chance of seeing them off. They scored early on from an interception and a charge down but after that they only managed a couple more penalties.
"We knew if we stuck to our guns, and the game plan, we would win the game."
It's a testing time for all the pro-clubs as players are called up for inter-national duty in the RBS 6 Nations but McGuigan says that the inter-nationalists know they'll have to fight for their place on their return.
"This time of the year tests all the teams strength and depth and we know we are in good shape in that area. We have some big games over the next few weeks and the guys who are starting those games know it's a good time to make the jersey their own."