Success-starved Leeds fans are revelling in the spotlight as another high-profile cup tie is set for a live national television audience, but Grayson does not believe Spurs' Premier League stars will be intimidated by a partisan home crowd.
Grayson said: "Most of their players will have played at Elland Road, if not for Tottenham then for other clubs and they'll have been aware of our fans at Old Trafford and at Tottenham, so I don't think they'll be in for any shock."
Leeds ambushed arch rivals Manchester United at Old Trafford in the third round before an inspired late rally at Tottenham sustained hopes of another big upset.
Both wins came courtesy of star man Beckford, with the Leeds striker taking his tally for the season to 24 with another brace against League One rivals Colchester on Saturday.
But a half-smiling Grayson suggested it was now time for someone else to step forward.
He said: "We'll just go and enjoy it. We've not really spoken about it. We'll just go and enjoy it like we did at Old Trafford.
"Give the best account of yourselves that you can, have no regrets when you come off the pitch and somebody try to be a hero again because Jermaine's got a lot of the headlines in the last couple of rounds, and it would be nice for somebody else to get them for a change."
Leeds have won some new friends under Grayson this season, but the former Blackpool manager stops short of agreeing they are ready to shed their reputation as one of the country's least liked clubs on the back of some favourable national coverage.
He said: "I'd like to think that we're trying to do something about it because of the way that we play.
"There's been a stigma attached to the football club for the last 30 or 40 years, justifiably so or unjustifiably so, that's down to people's opinions.
"All I'm trying to do as a manager is create a team that is hard working, has a desire to succeed and try to entertain as well, and if it means we're liked, well so be it and if we're not liked and are winning football matches, then who cares?"
Grayson will take heart, in that respect, from comments made by Harry Redknapp after the Tottenham boss had just seen Beckford's last-gasp equaliser deny his side passage through to a fifth-round tie at Bolton.
The Leeds boss added: "He was very complimentary about how we played. He was obviously very disappointed after conceding such a late goal and he made me laugh in his press conference when he said he'd love to come up to Leeds on a Tuesday night and wanted (Michael) Dawson to give away a penalty.
"That's Harry for you. He's a top footballing bloke and I'm sure he'll enjoy the experience at Elland Road on Wednesday night."
Leeds v Tottenham. Click here to bet.