Pulis is desperate for a win after seeing his side slip to within three points of the Premier League relegation zone, but he is aware that Sir Alex Ferguson's team will be keen to bounce back from Monday's 2-1 home defeat to Manchester City.
He said: "It's a game that we are looking forward to. This is why you want to be in the Premier League. We have given them good games here before.
"They have just lost against City, and I'm sure Fergie will have been at them this week. It will be incredibly tough for us.
"I accept that in life and in football, you have good times and bad times. It's how you deal with it that is important. Hopefully, with the background I have had, I will be able to see this through. It is a great challenge.
"You get no grace for what you have achieved, people look at what you are doing now, and what we are doing now isn't what we have done in recent years.
"Hopefully, fingers crossed, the lads will enjoy this challenge because we haven't had this before. We are desperate to succeed in it."
Stoke chairman Peter Coates said this week that he believes four more points should ensure survival and Pulis is keen to hit that target as soon as possible.
He said: "People question things when things aren't going well. I am fortunate to have a family in charge of the club who are fantastic.
"This week the chairman has been down and had a chat with the lads. He's a top man, and we are fortunate to have him here.
"The time has come for us to win a couple of games and put this right. Then we will look at what went wrong at the end of the season.
"You can't cherry pick games and look at ones where you will get points. It doesn't work like that. We have to go out and get the points.
"Things aren't going for us at the moment, but when that happens you have to work even harder, and that is what we are doing."