Swansea's victory against Sunderland has put pressure on both Hull and Crystal Palace to get a result.
Allardyce succeeded Alan Pardew with the Eagles 17th in the Premier League - although things got worse before they got better. "We put the boys at the first to believe and fight until this moment".
Palace, who have been transformed since the arrival of manager Sam Allardyce in December, host relegation rivals Hull City tomorrow. Silva arrived in January and, while securing some eye-catching home results, the Portuguese has gleaned only two points from nine away fixtures.
Hull: Eldin Jakupovic 5, Harry Maguire 6, Andrea Ranocchia 4, Michael Dawson 5, Ahmed Elmohamady 5, Andrew Robertson 6, Sam Clucas 6, Kamil Grosicki 6, Alfred N'Diaye 6, Evandro 5, Oumar Niasse 5.
They join Sunderland and Middlesbrough in dropping down to the Championship for the 2017-18 season.
On Sunday, if he can steer Crystal Palace to a point from the basement showdown with Hull City, Allardyce will once again have protected his record of never having suffered relegation from the Premier League. That the Tigers got so close to surviving was down to Mike Phelan's January successor Marco Silva.
But instead of cranking up the tension, Hull allowed Palace to coast their way to safety - and allowed Allardyce to toast his return after his ill-fated spell with England.
"I said to myself this would be the hardest one, given the quality of the teams we had to play on the run-in", said the 62-year-old.
"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.
The shock of the stumble last week at home to the Black Cats will be out of their system and this has been a team able to shake off a reverse and keep fighting in and around the foot of the table since Silva's arrival.
"Now, of course they're in a better position than us, but they need to do something to (make themselves) safe".
Crystal Palace will win their battle for Premier League survival, according to their former midfielder Aki Riihilahti, whose combative performances made him a cult hero for the club. His Palace side narrowly escaped relegation to the third tier in 2001, but experienced the joy of reaching the Premier League via the playoffs three seasons later. "Crystal Palace have an atmosphere and a stadium that isn't easy to play in and they are very strong in attack, causing problems for all teams".