Swansea took full advantage of Hull's defeat with a 1-0 win against Everton which put the Swans in the driving seat in the relegation battle.
"They (Sunderland) stopped Hull getting valuable points and also it shows us they're still working hard", Clement told a news conference.
Ahead of their game against Everton on Sunday (AEST), the club revealed that the players would cover the cost of match tickets for fans heading to the north east at the weekend.
"If there was ever a time that we need one another more than ever, it's now, over these last few games of the campaign".
Hull City's Andrea Ranocchia has claimed the Tigers "still believe" they can survive ahead of their crunch match against Crystal Palace on Sunday and has compared their final two games to Champions League finals.
A win against the Eagles could lift Hull out of the relegation zone, but only if Sunderland can keep Swansea at bay at the Stadium of Light.
Silva, a newcomer to English football, engineered such a dramatic turnaround that only two teams who were in the bottom half of the table when he arrived have outperformed Hull over the past 16 games.
It is a factor that Clement feels could prove decisive in the final two games, with the former Chelsea No. 2 seeing similarities between that and some of the players he worked with at Stamford Bridge.
Palace need a point against Hull at Selhurst Park to guarantee their own survival.
But head coach Clement, who was appointed in January as Swansea sat bottom of the league with 12 points from 19 games, insisted escaping relegation would be a source for celebration.
"We've got some experienced boys".
Even if Sunderland win their remaining three Premier League games this season, it will be their third lowest points total in a Premier League season (15 in 2005/06 and 19 in 2002/03).
But they have since started appearing online, and the club have warned anyone found making profit off the players' donation will face the consequences.
"The support we've had at home and away has been incredible considering how tough it's been at times".