After ensuring that they will be playing Premier League football for another season by picking up three points away to Leicester last week, Moyes' West Ham side battled hard to earn themselves a point and the Scottish manager expressed his delight with how his team performed.
“It was a good point for us,” he told the official club website. “Maybe Manchester United will say the same thing as well. We had one or two chances, but Adrian had to make some good saves too.
“I thought our boys showed a really good attitude. After getting safe in midweek you’re never quite sure [how you’re going to react], but they were bang at it and great credit to the players.
“I think the most pleasing thing was to get a clean sheet. If we’ve had a failing this season it’s been the amount of goals we’ve conceded, but we’ve kept two in a row now and that’s important.
“Young Declan Rice played very well tonight. Angelo Ogbonna did well again, Zabaleta, I think the boys at the back did a really good job.
“But we were a threat at times as well. With Marko Arnautovic up front we’re always going to be a threat to everyone we play.”
After West Ham were previously criticised for making a trip to Miami as a team-building exercise, Moyes also made sure to discuss how the trip had a positive effect on his side's successful relegation battle.
He added: "We took the players away after the Burnley game. We were criticised for going away, but it was the best thing we did. It pulled the players together and we worked hard when we were away.
“The players had a good time together as well, we all did, and since we came back we have been bang at it."
Moyes faces his former side Everton in West Ham's final game of the season on Sunday and he insisted that the east London outfit would be using the game as an opportunity to finish as high as possible in the Premier League table.
“We want to climb the league table, we want to be higher, so if we can win against Everton, great. But obviously we’ve done the job we came in to do, which was make sure we weren’t relegated.
“When we took over we were in a relegation position, we’re not now, and over that time the players have improved and the team has improved."