Marco Silva's Hull, who are unbeaten at home in their last seven league games, host 10th-placed Watford on Saturday.
"It is to do with the situation, there are five games left with three at home," Clement told a news conference on Thursday.
"Our form has been better at home than away, and the fact Hull are home to Watford, a game I believe they will win, we have to win.
"I hope the players respond, they have not responded well over the last six games when pressure has been there but we have to perform to alleviate it. Otherwise the last few games will be for nothing."
Clement, who previously worked as a coach and later assistant manager at Chelsea, said he would be interested in speaking to John Terry about a move to Swansea at the end of the season if they avoid relegation.
Earlier this week, Terry, Chelsea's most successful captain, said that he will leave Stamford Bridge at the end of the campaign.
"I would like to say, having worked with him, what a fantastic player he (Terry) is and what a career he has had," Clement added.
"If we stay up why wouldn’t we be interested? I know him well and would be more than happy to speak to him."
Swansea have a tough run of fixtures following the Stoke match as they face fifth-placed Manchester United and seventh-placed Everton before a crucial game against basement side Sunderland.
They host West Bromwich Albion in their final game of the campaign.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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