The goalless draw at Cardiff City on Tuesday left Paul Lambert's side four points clear of bottom three with 12 matches remaining.
"It's the best league in the world, so to be part of it is exciting," said USA international keeper Guzan. "But you need to be a man and stand up to the challenge and your responsibilities. And that as a footballer is to go out and perform.
"We don't feel under pressure. All you can do is look forward to the next match, not worrying about other results. You have got to take care of your own business."