In an interview in The Mail on Sunday, the former Manchester United manager also takes a swipe at the way he first heard the news of his sacking from the media rather than directly from the club.
He tells how he turned up at 4am on April 22 at United's training ground to train alone, knowing from the media he was about to be sacked but without having been told by the club.
Moyes was sacked after just 10 months in the role. His successor, Louis van Gaal, took charge of his first Premier League game on Saturday, when United lost 2-1 at home to Swansea City - a team they beat 4-1 under Moyes last season.
United slumped alarmingly under Moyes, eventually finishing the season in seventh place, but he feels he could have proven himself a worthy replacement for Sir Alex Ferguson if the club had shown more patience.
"It was a step into the unknown and, looking back now, it was near enough the impossible job," Moyes told the Mail on Sunday.
"I was devastated to lose the job because it was something I felt I could make a real success of. We knew it was going to take time to make the necessary changes. It was going to take time to evolve.
"But we were in the process of making other important changes. In the end, I don't feel I was given time to succeed or fail."
Moyes admitted that he had been hurt by the nature of his dismissal, which was widely announced in the British media before the Scot received official confirmation from the club.
"In the end it was difficult for my family, the way we discovered - via the media - that I'd lost my job," he said.
"We have always tried to do things the correct way. I know it comes with the territory, and I know if you lose matches you risk being sacked. But how it affected my family made it hard."
Moyes' chances of success at Old Trafford were undermined by the fact that he and incoming chief executive Ed Woodward missed out on a number of targets in the transfer window prior to last season.
The 51-year-old, who is looking for a new job, confirmed that United had shown interest in Cesc Fabregas, Gareth Bale and former player Cristiano Ronaldo, only to miss out on all three.
"It's been well documented that we wanted Fabregas, Bale and Ronaldo," Moyes said. "There was talk of Ronaldo when I first arrived. We were close to getting a couple of major names.
"I'm not getting in a blame game here, but things just didn't materialise. I had taken over from the most successful manager in history.
"The chief executive had taken over from one of the most renowned administrators in the game (David Gill). So it was a new job for two people."