Moore said: "When Crystal Ocean came to him, he dug in. He's done very little wrong in his career and has progressed from race to race.
"It was a really hard race, but he didn't look like a horse who'd had a hard race. I just feel it was a very good Leger - in normal years the first three would be worthy winners.
"He's shown he stays well, but he's an Irish Derby winner and that form looked very good. Everything had every chance, but he fought them off and was the best horse."
On winning the race for the first time, he said: "It means you have to win it again, really."
O'Brien, winning his fifth Leger, said: "We were all delighted with him. He had a little blip at York time (when he missed the Great Voltigeur). We were a little worried coming here, but Ryan gave him a class ride.
"We knew if we set a good pace for everyone we'd find out who the best horse was in the straight.
"He's a horse with a lot of class, which we saw in the Irish Derby. When Ryan wanted it, he gave it to him.
"Seamus (Heffernan) rides him a lot at home and has always been a big believer in him. He always said he had class and that he would stay.
"Ryan had ridden him once before when winning the Beresford on him, but that was last season. I was a bit worried about that as well, but it all went great."
He added: "As he had a blip at York we were worried coming here, but that he would improve a bit for the run. We had it in our heads that if all went well today and everything went well after he could run in the Arc.
"Obviously the lads (Coolmore) will decide what they want to do - run him again or put him away.
"He's probably a mile-and-a-half horse with class, so he'd have no problem going a mile and a quarter.
"He has a great cruising speed and we always thought he had courage and stamina as well as class."