USP s fairytale run in the competition continued with a 2-0 last-eight victory over Hellenic League Premier side Flackwell Heath.
Goalkeeper Price, 31, revealed both he and older squad members - captain Tom Jeffes and Andrew Todd - have been trying to keep excitement levels down of the younger players throughout a sensational run.
The established trio have been offering reminders to play each game on merit and not be overawed by the occasion.
Price thinks fixtures being held behind closed doors because of the pandemic has actually benefited USP who now stand just 90 minutes from Wembley.
But he believes trying to calm the squad down in training this week and in the build-up to the semi-final against Hellenic League Premier Binfield will be very tough.
Price, who kept his first clean sheet of the Vase run against Flackwell, said: 'Me, Jeffers (Jeffes) and Sweeney (Todd), we always chat about how we can assist everyone else and stuff.
‘It’s one of them where you sort of say to the players at training not to change anything they do normally, it’s just 90 minutes.
‘Who cares if you’re playing against Arsenal under-23s whoever it is, it’s just 90 minutes at the end of the day.
‘It’s just about relaxing, enjoying it - it was nice to see some fans out by Gunwharf watching over the fence (against Flackwell) - it was set up perfect.
‘With the no crowds, apart from losing out on all the gate money, I genuinely believe it’s helped us.
'It’s just trying to calm them down, but it’s going to be very difficult this week.'
Price was in no doubt Flackwell were the toughest opposition USP have faced in this season's fairytale run.
But goals from top scorer James Franklyn and Harry Sargeant ensured a sixth higher division scalp in seven rounds.
And Price believes USP's management team played a clever tactic by withholding some information from the players prior to kick-off.
He said: 'We didn’t get told by the management, Glenn (Turnbull), Fraser (Quirke) and Barto (Paul Barton) withheld that they had some step 2 players playing.
‘They kept that away because of the nerves.
‘They were the best opposition we’ve come across in the FA Vase, without a shadow of a doubt.
‘Obviously, Tavistock the week before had been the best we’ve come across; no disrespect to Portchester, Christchurch or anyone else, but because they’re local we knew a bit about them and their players.'