The Eagles found themselves dragged into a three-team battle to avoid the drop following a run of three successive defeats in recent weeks.
Allardyce's proud record of having never been relegated in his 23 years of management lives on, but he believes that keeping Palace up was the "hardest" of the lot.
"I think because of the run-in, the size of the teams we have had to play, this was the hardest," he told Sky Sports News. "Now, we have not wasted the magnificent results we have achieved, particularly in that short spell where we did well against Chelsea, Liverpool and Arsenal.
"It is a massive relief that's for sure. We all knew the implications of relegation today and the devastation it causes a football club and this football club has stayed in the Premier League for five years and wants to grow. It was a great effort from the players today.
"Tactically we set out to nullify Hull City and just expose them when we thought they were weak, which is they held a high line and put a quality ball in behind - obviously that got us off to a great start with the first goal. It was a perfect performance from the players today, 4-0, a clean sheet and it is terrific for everybody that has taken part since I've been here.
"We had a little slip-up but that came through injuries really and now we have come back, in our last home game, what a way to finish in front of your home fans. I know it puts Hull down after a brave fight but it is a great, great feeling."
Palace, who see out their season with a trip to face Manchester United next weekend, equalled their best ever winning margin in the Premier League with the four-goal victory over Hull.