The Scottish coach succeeded the legendary Sir Alex Ferguson in the Old Trafford hot seat in 2013 but was sacked after a disastrous 10-month tenure and he knew that the club would be in for a period of upheaval as soon as he arrived.
Moyes told the Stick to Football podcast: "I had a feeling that it was going to take a long time to fix (Manchester United) but I couldn't come out and say that it's going to take six years to fix.
"The team had just won the Premier League, and I was thrilled to be taking over, thinking this is great, but I did feel like I was going to take a longer time to change things around."
Moyes believes the struggles of his successors - including Louis van Gaal and Jose Mourinho - to restore United to former glories shows that there are deep-rooted problems at the club.
He said: "I hear people talk a lot about Manchester United and think to myself, Louis van Gaal and Jose Mourinho would arguably be right up there in the top dozen managers worldwide who you'd want to be manager of your team, and they found it impossible to get what they want. It might run deeper than that (the issues at Manchester United)."
Despite his bruising experience at United, Moyes enjoyed working in such a "tough" dressing room where players weren't afraid to make their voices heard.
He said: "I have no regrets, I learnt so much from the players, the level of fight they gave you - the dressing room was tough, and they called each other out, there was no messing around in the months I was there.
"I admired them greatly and could see why they'd been at the top but there was a diminishing level of quality and age. They had a toughness and ability to dig each other out, which is lacking greatly in the modern game."