The Potters' cup trip to Derby on Saturday is swiftly followed by Tuesday's league clash with Manchester United at Old Trafford.
Pulis' side then face another top-flight contest four days later when they host Sunderland, and the Welshman said: "This round has been lined up with two Premier League games following it, and it shows what other people think of the FA Cup.
"That is disappointing, to have it as part of a three-game week, but we will approach it in the right way and hopefully we will get the result.
"As soon as the game is over with, we will be preparing for Manchester United away, but that is the one disappointment - with the FA Cup, you would like to have a bit of time after it and you haven't, because they have put a Premier League fixture in straight away afterwards."
When it was pointed out to him that Tuesday's match also coincides with the January transfer window deadline, Pulis said: "I didn't want to bring that up, but that shows how well organised it is.
"You make plans with great difficulty, but then that is the people running football."
Although there are plenty of other things to think about, Pulis has been keen to stress that the FA Cup - which seems to have dropped down the list of priorities for so many clubs in recent years - is important to Stoke.
The 54-year-old, who guided the Potters to the final of the competition in 2011, said: "We had a great time last year, getting to Wembley twice, including an FA Cup final for the first time in the club's history.
"This is a local derby and it will be a great game between two old-fashioned clubs in lots of respects.
"We've got great and fond memories of last year in terms of what it brought the football club and what it brought for us individually and for the supporters.
"To go and win this game of football is important to us."
Pulis is looking for a positive reaction from his players at Pride Park after what he described as a "tepid" performance from them in last weekend's 2-1 league defeat to West Brom at the Britannia Stadium.
He has been encouraged by their efforts in training since then and has virtually a full squad to choose from for the encounter with Nigel Clough's npower Championship side.
The Rams are unbeaten in their last six matches in all competitions and Pulis, who made six changes to his first XI for the Potters' 3-1 third-round victory at Gillingham, has vowed to pick a "strong" side for what he is anticipating will be a tough assignment.
"They are on a great run and look a very solid, young team. Nigel has done a great job there," Pulis said.
"I will pick a strong team for Derby - I think I have to. We have to respect them for what they are doing.
"I think the team we put out will reflect what we think of the FA Cup."