Bournemouth boss Eddie Howe said his side have experienced "a really difficult run".
"We've been knocked quite a lot this season with the injuries and the run that we've had. We had players playing who were not 100% fit," he added.
"It was a fantastic effort," Hodgson said.
"I thought Jordan did ever so well to set up the first goal.
"The second was one of those wonderful individual efforts that will live long in the memory and get lots of airings on TV.
"I can't divide myself from the team," said Pellegrini. "For West Ham it was an important three points.
"I said before the game that I felt every day the commitment of the players in the work that they do.
The former Millwall and MK Dons keeper sank to his knees before celebrating in the stands with his father, who played in the West Ham defence for 21 years.
"It still doesn't feel real," said Martin, who is a boyhood fan.
Tottenham manager Jose Mourinho says he would "hate" anybody to say he had made an impact after their 3-2 victory at West Ham in his first game in charge.
"It's not about me, it's about the players and club.
West Ham manager Manuel Pellegrini: "I don't know if it was an unacceptable performance. We conceded the first goal from a corner that was not a corner.
"When you concede so many easy goals, it does not help.
West Ham manager Manuel Pellegrini: "It is really difficult to explain why we played the way we did in the first 45 minutes.
"The last two games we played at home we started by pressing from the beginning, playing in the opposite half.
West Ham manager Manuel Pellegrini speaking to MOTD: "In football, you must score. We dominated the game and tried to create options to score.
"We had two or three chances and must decide the game by scoring.
West Ham manager Manuel Pellegrini, speaking to BBC Match of the Day: "It's hard to accept. We were a bit unlucky with the decisions.
"We scored a goal and took the lead but we had other chances, especially in the first half.
Left-back Aaron Cresswell fired in a late equaliser at the Vitality Stadium as West Ham stretched their unbeaten Premier League run to six matches.
Bournemouth manager Eddie Howe: "It was another for the neutral, who'd have loved it.
Andriy Yarmolenko's opener was added to by Aaron Cresswell's beautiful free-kick as the Hammers got all three points against Manchester United
West Ham United manager Manuel Pellegrini says his side are becoming "more consistent" after they beat Manchester United 2-0.
Aston Villa moved out of the relegation zone by drawing against a West Ham side who finished with 10 men after Arthur Masuaku's red card
West Ham boss Manuel Pellegrini disagreed with the decision to send off his left-back.