Swansea travel to already relegated Sunderland after the Everton game before ending their season at home to eighth-placed West Bromwich Albion.
"We know that if we manage to survive this year it will be a remarkable achievement," Clement told a news conference on Thursday.
"It has not been done often. Anything worthwhile you have to work hard for. You have to go through an ordeal with all the pressure, and we certainly will have done that," he said.
"We have got to three games left now, and we have to try to win all three of them."
Fourth-bottom Hull City have a two-point lead on Swansea, but Clement is counting on his team's recent improvement in form to keep them within touching distance of survival.
Swansea snapped a three-game losing streak by beating Stoke City 2-0 on April 22 and followed that up by snatching an unlikely draw at fifth-placed Manchester United in their last league outing.
"Our form is good," Clement added. "We played well against Stoke and then again at Manchester United, so we go into the game with a lot of confidence.
"If we can get three points against Everton, that will maintain the pressure on Hull. They play before us so we will know their result. The following weekend we play first, so it will be interesting over the next couple of weeks."
Winger Jefferson Montero may not play again this season after damaging his hamstring at United, but defender Martin Olsson is available for selection after recovering from a similar injury.
(Reporting by Simon Jennings in Bengaluru; Editing by Hugh Lawson)
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