Moyes has transformed the Hammers this season and, ahead of Sunday’s match with Arsenal, they sit fifth in the Premier League .
Before that, though, the Scot was having a difficult time after being sacked by Manchester United and Real Sociedad, and resigning from Sunderland.
Arteta has revealed seeing Moyes struggle pained him, with the Spaniard a big fan of the 57-year-old after playing under him at Everton.
“I suffered when he had a difficult time because I didn’t think it was very fair on him that he was given no time in some places,” he said.
“I know about his qualities and I’m glad to see that now he is enjoying it and doing what he is really good at. I can see his team being what he is and what he likes to do.”
Arteta still enjoys a good relationship with Moyes and the pair remain in contact.
“He was the one that introduced me to the Premier League and he has been a huge influence,” said Arteta.
“First of all on a personal level because I think he made me a better person, made me mature in the earlier stages of my career.
“He was really demanding and challenging but at the same time really, really supportive.
“I learned a lot as well as a footballer, I think he made me a much more complete player, he made me play in different positions and gave me a lot of responsibility as well. I have great memories with him and we had some great times together.
“I really liked how he managed the group as well as the individuals. He really installed a real belief around the club to be together all the time, to look after each other and nobody was more important than the team.
“He really created a special atmosphere when we were together and I think that is why everyone involved at that time really enjoyed our time together.”
West Ham’s form this season has them dreaming of a European finish and Arteta believes that would be “an incredible step” by Moyes.
He added: “They are not too far off achieving that, there are still a lot of games to play but they are in the right direction.
“The team is looking really solid and strong and as well with some real quality when they have time to play and when they are attacking the opponent.”