City were 2-0 up within the opening 15 minutes, Nigel de Jong powering home his first goal for the club and then Pablo Zabaleta guiding a shot on target beyond Robert Green which Lars Jacobsen inadvertently blasted into the net as he attempted to kick the ball away.
The Hammers hit back in the 33rd minute through Demba Ba, but it was the hosts who looked more likely to score another after the break and deservedly held on for all three points.
"We made a very bad start - in the first 20 minutes we were not in the game, they had scored two goals and could have scored more," Grant said.
"We had a great comeback and showed a lot of spirit and the character of the team, and we made it 2-1 - also Robbie Keane had a big chance.
"In the second half we could have done some more, so there were a lot of positives to take for the next games, which are the most important ones."
The Hammers, who are three points from safety, play Blackburn, Wigan and Sunderland in their final three games and Grant has set a target of at least seven points from those fixtures to beat the drop.
Source: PA
