United, 12 points clear at the top of table with seven games to play, are striding towards a record-extending 20th title while the Potters struggle at the opposite end.
Sir Alex Ferguson's men did suffer defeat to rivals Manchester City in their derby last Monday but Pulis sees that as a mere blip.
He said: "I think you have got to recognise the strength they have got. You have got to recognise you are competing against overwhelming odds in a lot of respects.
"That is why they are champions-elect - they have got the best team and the best players.
"We have to pick a team we think will work as hard as they possibly can to nullify their strengths, and also give us an opportunity to compete at the other end of the pitch as well."
Alarm bells have started ringing at the Britannia Stadium after a dismal run of just one win in 13 league games.
But in a 21-year managerial career that has taken him through the divisions, Pulis feels he is equipped to deal with the challenge.
"I think publicity-wise it is the hardest time I've had - but I have had tougher times with teams that haven't been as good as this one, and you've had to eke out results," said Pulis, who has managed six clubs.
"But everything that goes with the Premier League is magnified and multiplied enormously. We have to concentrate on ourselves and not take too much notice of what is going on around us."