The 3-1 win over Newcastle on the final day extended their unbeaten run in the league to nine games as they once again recovered from a slow start to the season.
"The way I have been brought up you celebrate finishing first and maybe in the Premier League you celebrate if you finish in the Champions League or Europe," Moyes said.
"But nevertheless, from where we were in October or November, and given the teams we were behind, it's been a brilliant achievement from the players.
"Anyone who's watching us now, we're purring. We played some top stuff and have played in that fashion for the last few months really. It was really good to watch."