Magpies' FA Cup success means they are there to be shot at in the National League North
The victory over the Rams comes off the back of wins over Football League outfits Wigan and Peterborough in previous rounds and has resulted in them being paired with Premier League Wolves in the fourth round at Victory Park.
While the Magpies can be proud of their successes over higher-ranked opponents, it ultimately counts for nothing when they return to league action.
And as Vermiglio concedes, clubs in the National League North may head into contests against his men with the psychology of looking to knock them down a peg or two.
Leamington were a perfect example of that on Tuesday as they returned from Victory Park with a hard-fought 2-1 win and Celtic will be aiming for something similar this weekend.
“Clubs will see our results in the FA Cup, see all the media attention and the stuff about our singing of Adele’s “Someone Like You” in the changing rooms afterwards – they will crack a few jokes about it and use it to their advantage to spur themselves on against us.
“They will probably think, ‘Let’s show these lads’. Doing well in the FA Cup can work against you but that is the challenge for us.”
Vermiglio made a number of changes for the visit of Leamington.
Scorer of the opening goal against Derby Connor Hall missed the game after limping off against the Rams, while Andy Halls and Harry Cardwell were both on the bench nursing knocks.
Vermiglio admitted all the outside distractions surrounding their win over Derby and the subsequent cup draw did have an effect on their preparations.
But even still, he felt his side’s first-half performance was as good as anything they have produced this season and was pleased to see players come into the side and produce.
He is hoping his side can find a similar performance this weekend against Celtic, but this time be on the right side of the margins.
"It must have been difficult for the lads because you want to enjoy the occasion and from the Saturday even to Tuesday, a lot of the lads were still speaking to the media.
"They were still really on a high with it all.
"So it was possibly a distraction and not the correct build up going into another game.
"But at the same time, this is the moment that the players are in and you can't really blame them, you just have to do your best to channel it.
"Having said, the first 45 minutes against Leamington was probably the best we have played without scoring the goals that we should have done.
"The performance the lads put out was very, very good.
"But credit to Leamington, they hung on and stuck with it and ended up winning a penalty to win the game."
The Magpies are three places below Celtic in the table, but can leapfrog above them if they claim all three points this weekend.
“I know Celtic’s manager Adam Lakeland has put together a good side,” Vermiglio said. “They usually play with a back three.
“They are a good side, can move the ball but also have a physical presence.
"It's going to be a tough game for us but if we are to be up there at the end of the season, we need to be beating teams who are in and around us in the table."
Meanwhile, Chorley's home game against Kettering on Tuesday night has been postponed due to the Magpies' FA Cup tie against Wolves the following weekend.