Moyes accused Chelsea winger Florent Malouda of stamping on Neville but praised the response from his side following last week's 4-1 home drubbing by West Brom.
The Everton defender's decision to get up immediately from the altercation almost certainly saved the Chelsea winger from a potential red card.
'I have got to say Phil Neville did fantastic,' said Moyes.
'Malouda came in and stamped on him but Phil got up and ran away. But a minute later one of their players went and got him booked for nothing.
'It was disgusting. He helped keep Malouda on the pitch and a second later one of their players goes down easy and gets Neville booked. Ridiculous. But you need to have a look at Ivanovic's tackle in the 31st minute as well and look where the referee was.
'The second half we deserved the result. Chelsea had a few chances but then you expect that. It was tough for us in the first-half.
'The quality of our decisions in the final third probably cost us winning the game.
'But the players responded really well today. The players here tend to do that in the right fashion.'
Chelsea's first half penalty was awarded after goalkeeper Tim Howard brought down Nicolas Anelka but Moyes agreed with referee Lee Probert that it didn't warrant a red card.
'The goalkeeper could not get out of the way,' added Moyes. 'If it was me, I would want a penalty kick for it. But it definitely was not a sending off.'
Meanwhile, angry Chelsea coach Carlo Ancelotti labelled his side 'frightened' after a shocking second half display cost them the chance to go back to the top of the Premier League.