Chelsea had skipper John Terry sent off int he first half for a challenge on Leon Osman.
The Toffees had a goal by Steven Pienaar disallowed in the second half.
“I felt the referee and linesman got that decision (the disallowed goal) right,” said Moyes. “Many managers may not say that.
“But I felt it was just offside and the ball could have just been in Petr Cech’s hands as well, so from that point of view, the officials were right.
“My first reaction from the sidelines was that the tackle for the sending-off was reckless.
“It was going to be close. In my day I would have enjoyed a tackle like that, but they won’t allow them now.
“The referee did well. Did he get the big decisions right? Yes, he did. The tackle for the red card was not good, and the disallowed goal was also the correct decision.”