Gaffer hails Jermaine Beckford's display
The Toffees were trailing at Goodison Park after Ivan Klasnic had given the Trotters a the lead, and with less than five minutes to go the Belgian was dismissed for reacting angrily and kicking out at goalkeeper Paul Robinson.
However, substitute Jermaine Beckford - who had come on for Phil Neville - managed to score a late goal to ensure that his side took away a share of the spoils.
This also ensured that the hosts continued their unbeaten run, which has stretched to seven games now.
"It was correct," Moyes told reporters, concerning the sending off. "I thought it was a foul on Fellaini, the tackle by Robinson, which I thought might have been a booking.
"But I've no complaints, it was retaliation. He shouldn't do it, he was stupid."
Beckford's goal was his first in the Premier League, and the gaffer had a lot of praise for the forward - who made a jump from the League One to the top-flight.
However, the manager maintained that the striker still has a lot to learn to complete the transition from playing in the third tier to putting in consistent performances at the highest level.
"Anyone who has watched Leeds United over the last few seasons will tell you he can score an array of goals," Moyes said.
"It was a fantastic finish, it really was. We needed something, it was probably the last 10 or 15 seconds of the game.
"I think that is what Jermaine has got but there is a lot he will have to learn in being a Premier League player.
"I put him in a bit earlier than I should have done. My idea was always to bring him off the bench in games where we needed a goal.
"I shouldn't have started him so early, that was a mistake of mine, but it was a good goal. The one thing we can't teach him is the one thing he came with, the ability to score goals."
At the end of the day, Moyes felt that the performance put in by his charges warranted a draw.
He said: "If we hadn't got a point, we'd have come away saying it wasn't right."
Everton now take on Arsenal over the weekend.