But the Blues manager admitted he had been bracing himself for a heavy defeat!
'The players were great. I was concerned before we came down here. To come to Chelsea and get a result is a great one,' he declared.
He picked out the makeshift central defensive pairing of Lucas Neill and Johnny Heitinga for special praise, after the duo went head to head with the in-form Didier Drogba and Nicolas Anelka.
'They were great and did a very good job today,' he added. 'They stuck at their jobs, they're both experienced enough and we needed that today.
'It was one of those days where I thought we might have to take a sore one and I didn't want that.
'We're trying to regain a little bit of confidence; the players did that today and hopefully we can build on that.'
Moyes believed the 3-3 draw was his team's best result of the season.
'It was a great draw for us,' he added. 'I'd have certainly taken a draw before the game with the team that we had out.
'They didn't half show great resilience and endeavour. We know the quality Chelsea have got, and we know that at the moment we can't match that.
'I have to give great credit to the boys that played today. I thought they were immense.
'Chelsea have very few weaknesses. Undoubtedly they are in the top three teams in this country and the same in Europe. They have very few weaknesses, and I thought today we kept at it.
'The team showed a great spirit and that's what we've tended to do at Everton.
'I'd say this was our best result of the season. Chelsea caused us lots of problems but I think we're entitled to that bit of luck.'
Chelsea counterpart Carlo Ancelotti rebuffed suggestions that Chelsea are in crisis after some desperate defending from set-pieces allowed Everton back into the match.
'Who can say we are in crisis?' asked Ancelotti. 'I don't think so. I want to be objective and when I look at the game and the way we played I saw that my team played very well.
'We didn't win because of mistakes at set-pieces. But we played very well for 90 minutes with intensity and good concentration.
'We created a lot of chances to score and were unlucky today. I am happy because Chelsea played very well for 90 minutes, (but) I am unhappy with the result. I didn't have to say anything to my players because they did the maximum.
'We didn't win but that can happen in football - you can draw at home.