Moyes has managed to steer Everton clear of the dropzone after succeeding Dyche midseason.
Dyche told talkSPORT: "I left it in good hands. I've left it in good shape. I said that and I got batted for that as well. I said it was in good shape. Moysey has taken over and he knows it and he gave me a shout out about it.
"I said to him they're in good shape. They're fit, but the weight of a club sometimes gets too much. I think for the players it got too much. You know I was okay with it. I learnt about the size of the club and the feel and the weight of it, I was alright.
"But you could see it in the players, and it was time for me to go and have a chat with Kev Thelwell (director of football) and go, 'Listen, this is what I'm seeing, this is what I'm thinking'.
"I'm putting it out there for the club because I insisted that it was in a better shape when I left than when we got there, we'd come through the challenges.
"And I knew deep down, they just needed a new... Football's a weird business, sometimes you just need a new voice. You know, small details can change, a new manager going in. And Moysey, who I admire a lot, I think he's a fantastic manager and a good bloke as well.
"Spoke to him as well, by the way, very open about that. I told him there's a lot of good there, and I'm delighted for him, I'm delighted they're going well."
Dyche also remarked: "You know what I can't get my head around, people go, 'Oh, you must be disappointed they're doing well'.
"What? After two years of grafting out, why would I want them to struggle, why would I want failure? We fought to keep it right, I wouldn't want it to do anything else than be successful.
"There's not a single bone in my body of any resentment, any anger, nothing like being gutted they're doing well. I wish them well."