Hodgson reckons Palace are safe after Leicester rout
Palace are 11th in the table, six points clear of 18th-place Southampton who have a game in hand, and Hodgson will take his side to Stoke City before they entertain bottom club West Brom on the final day of the season.
The win over Leicester was Palace's third in six matches and extended their unbeaten run to four games.
Hodgson, who picked out Ruben Loftus-Cheek as his side's star player on the day, said: "The important thing about today was that the pressure was on us. We had to make sure that it was transformed into points.
RH: The important thing about today was that the pressure was on us. We had to make sure that it was transformed into points. pic.twitter.com/rOApfqq9gK
— Crystal Palace F.C. (@CPFC) April 28, 2018
"We made certain that the quality of the performance led to goals. That was very satisfying and it was a great.
"With 38 points and a good goal difference I think we will be okay. It's dangerous to some extent because miracles do happen.
"You'd need to be Billy Beane to work out all the mathematical possibilities. I always thought if we got to 36 points with a good goal difference, we'd have a good chance of staying up.
"I am very proud of the work that has been done at this club since September. I want to share that with my staff and the players."
Leicester boss Claude Puel reflected on a hamstring injury to Wilfred Ndidi and a red card for Marc Albrighton as key moments in his side's defeat.
The Foxes were already 2-0 down by the time they lost Ndidi and Albrighton following goals from Wilfried Zaha and James McArthur, and Palace added three more in the final 10 minutes through Loftus-Cheek, Patrick van Aanholt and Christian Benteke.
"At 2-0 we lost all the balance to the team and there wasn't enough desire," said Puel. "We tried to change it tactically at half-time, but the injury to Ndidi and the red card made it really difficult. Tough day.
"The red card was harsh. It was a battle between two players, both making contact. It happened during a crazy five minutes with the injury to Ndidi that left the team so imbalanced. We needed to react in the second half and this scenario made it impossible.
"We didn't show enough intensity or desire during the first half, Crystal Palace played well and took confidence from that. We need to make sure our attitude is right during the remaining games of the season."