Andrea Ranocchia's failed clearance gave Crystal Palace's Wilfried Zaha an easy goal in the third minute, and the Tigers never recovered from having to play from behind the eight ball from nearly the beginning.
Palace winger Wilfried Zaha said: "It is massive, this win".
"We'd prepared for a final and then we made a mistake after a few minutes".
Sam Allardyce has maintained his remarkable record of never having been relegated from the top flight after Crystal Palace secured their place in the Premier League for next season. "We tried but conceded again and it finished the game". We'll see [if I will be manager next season].More news: Hawaii-bound passengers noticed unruly man before take-off
Hull City were relegated to England's second tier Championship on Sunday after a 4-0 thumping at Crystal Palace.
"Now is not the moment to talk about the future of the manager", said Silva, understood to be a target for Southampton should they look to replace Claude Puel.
After Swansea's victory over Sunderland on Saturday, the Tigers had to win at Selhurst Park to take the battle for survival to the final day of the season.
It's easy (to see) what the club needs to do differently.More news: Meghan Markle accompanies Prince Harry to Pippa Middleton's wedding reception
'I enjoyed these four months in the Premier League. Giving them a goal so early on and we were 2-0 down at half time. I came here with one idea on my mind and we worked hard every day to try and improve.
Three wins from their first three games got Wanderers up and running, but a run of 12 games without a win either side of Christmas left them in trouble. The 62-year-old Allardyce earned promotion with Bolton in 2001 and kept the northwest team up six times, and has since steered Blackburn, West Ham and now Palace to safety.
Palace had no reason to play with ambition, knowing their visitors required a minimum of two goals, and defended with the organisation Allardyce has given them.
Defender Andy Robertson says the Tigers paid the price for a poor first half of the season when they picked up just 13 points from the opening 20 games. "He has done a fantastic job to get them this close to staying up". "We'd been behind Hull for long periods so it's been the ideal time to put our best run of the season together".More news: Cloud Computing takes Preakness as Derby victor Always Dreaming fades
The Portuguese manager had arguably performed a minor miracle in stretching this team's Premier League aspirations even into the penultimate weekend, with players sold in January and a state of inertia in the boardroom.
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