Video: After Man Utd, can Leeds make it a Spurs double?
United, the last name pulled out in the fourth-round draw, were paired away with Spurs.
"We have a long season in terms of games but hopefully a successful one as well," Grayson said.
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"It's a good draw again. We're up against a top Premiership team and a top manager and we'll approach that as we have done for the Manchester United game – with the respect that they deserve.
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Hide Ad"But we've got a few league games in between and that's our bread and butter."
Burnley will travel to Liverpool, assuming Rafael Benitez's team win their replay at Anfield against Reading, while last year's beaten finalists Everton await the winner of Nottingham Forest's replay against Birmingham.
If Sheffield United can win their replay at Queens Park Rangers following yesterday's
1-1 draw at Bramall Lane they will travel to face Premier League Bolton.
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Hide AdDoncaster Rovers, whose tie at Brentford was postponed at the weekend, will be away again should they beat the Bees – to either Millwall or Derby.
Holders Chelsea face a trip to Deepdale to take on manager-less Coca-Cola Championship side Preston, who slaughtered Colchester 7-0 on Saturday.
Arsenal, who came from behind to defeat West Ham 2-1 at Upton Park, face another trip to Premier League opposition – Stoke.
Manchester City travel to Championship side Scunthorpe, and Aston Villa take on League One Brighton.
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Hide AdFulham must face the winners of Accrington's tie against Gillingham, while Wigan go to either Notts County or Forest Green – the last non-league team left in the draw.
4th round draw
Southampton v Ipswich
Reading or Liverpool v Burnley
Millwall or Derby v Brentford or Doncaster R
Bristol City or Cardiff v Leicester
Stoke v Arsenal
Notts County or Forest Green v Wigan
Scunthorpe v Man City
West Brom v Plymouth or Newcastle
Everton v Nottm Forest or Birmingham
Accrington or Gillingham v Fulham
Bolton v Sheff Utd or QPR
Portsmouth or Coventry v Sunderland
Preston v Chelsea
Aston Villa v Brighton
Wolves v Crystal Palace
Tottenham v Leeds U
Ties to be played weekend of January 23-24.