Moyes branded Everton’s performance as ‘special’.
“Chelsea have attacking options all over the field, as we know, and really good players, so it was going to be difficult,” Moyes told Sky Sports.
“But to come here and get a draw, especially with the players that we played today and the team we had out, I thought was terrific.”
Two of Everton’s goals came from free-kicks and Moyes added: “I think sometimes the key is just to get a good delivery in the box and you’ve always got a chance of scoring.
“It paid (off) for us today, in recent weeks it hasn’t.
“But I’m glad it did because I thought we deserved it for our endeavour, the way we stuck at it, our resilience at times in the second half.
“We never gave in when we went behind even with all the pressure we were under at Chelsea. The players certainly kept doing their job and stuck to the task.”
“I’m not saying people should be surprised – I think more surprised because of the team we had out today – to get a result at Chelsea,” he added.
“And myself, at times, I was looking at it and thinking for us to come to Chelsea and get a result with this team today will need something special.
“But we got something special with a top performer in Louis Saha up-front, ably marshalled by Brazilian Jo and then Yakubu and the rest of the boys behind them made sure they did their job.”