Beckford struck his first Premier League goal deep into injury time as 10-man Everton grabbed a 1-1 draw in a dramatic late finish at Goodison Park.
Ivan Klasnic had given Bolton the lead after 79 minutes and Everton's night had looked like ending in misery when Fellaini was sent off for kicking out at Paul Robinson four minutes from time.
Moyes has shown great patience with Beckford, who has struggled with the step up from League One since his summer move from Leeds, but concedes he expected too much too soon.
Moyes said: "Anyone who has watched Leeds United over the last few seasons will tell you he can score an array of goals.
"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."
Moyes had no issue with the red card shown to Fellaini, who reacted petulantly after a heavy challenge from Robinson.
"It was correct," Moyes said. "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."
Everton squandered a number of chances throughout the game to take the lead, with the otherwise vibrant Louis Saha spurning several on his first start since August.
Yet while the Toffees were disappointed not to take three points, the result at least extended their unbeaten run to seven games.
Moyes said: "If we hadn't got a point, we'd have come away saying it wasn't right."
Beckford's stunning late intervention denied Bolton fifth place in the table but manager Owen Coyle reflected pragmatically on the result.
Coyle said: "If someone had offered me four points from two games against Tottenham Hotspur and Everton I would obviously have taken them with both hands.
"I am disappointed because we were in a great position to win the game - but that is the only disappointment.
"I felt my group of players were terrific. Every one of them had to stand up to be counted.
"Goodison Park is one of the toughest venues in the Barclays Premier League and during the game we had to withstand periods of pressure.
"Everton are a good side with good players."
Coyle refused to heap blame on Lee Chung-yong, who lost the ball prior to Beckford's goal.
He said: "He has made a mistake in the 94th minute but he is a young player and he will learn from that and get better.
"He has been terrific for me from day one but I said to him at the end of the game we will learn from our mistakes and grow together as a team."