The Potters face United tomorrow [Saturday] at Old Trafford, where they have been beaten by Sir Alex Ferguson's men on all four of their visits since their promotion to the top-flight in 2008.
Overall, they have lost seven and drawn one of their eight Premier League meetings with the Red Devils and reflecting on one of them - played in Manchester in January 2011 - Pulis said: "We got close. Nani scored and we got beaten 2-1.
"We probably played as well as we have played. We have had good periods in games up there, but they have always managed to get goals at the right time.
"The most important thing is that you go out there and do your best, but it is not a level playing field when you are playing against the top six or seven sides - you just look at the players they have, the money they have spent and their turnover compared to other clubs in the Premier League.
"United are one of those sides, but we will go up there and do our best - it is all we can do."
Within their seven league games this season, Stoke have already faced Arsenal, Manchester City, Chelsea and Liverpool.
It has made for a tough start to the campaign which continues with tomorrow's [Saturday] match, before the Potters go into a less daunting-looking sequence of fixtures where they are scheduled to play Sunderland, Norwich, QPR, West Ham and Fulham.
"We go to Old Trafford, which will be a real tough one, and then we are through that run of games," said Pulis, whose team have only suffered one loss - against Chelsea - in the league so far this term, drawing five times and beating Swansea.
"The other games we will play will be really tough because they are Premier League sides, and I have the greatest respect for this league and every team in it.
"But there are clubs without a question of a doubt that are on a different level to what we are, and we will have played five or six of them after Saturday."
Pulis will assess the condition of Glenn Whelan and Michael Owen ahead of tomorrow's game against the latter's former club.
Midfielder Whelan, who came off in the 0-0 draw at Liverpool with a hamstring problem which kept him out of the Republic of Ireland's World Cup qualifiers against Germany and the Faroe Islands, is rated by Pulis as having a ''50-50'' chance of featuring at Old Trafford.
The manager has also said he expects striker Owen, missing from the Liverpool game after tweaking his groin, to only be fit enough for a place on the bench at best, but defender Andy Wilkinson is available again after completing a three-match suspension.