Stubbs, who captained the Blues to a fourth-place finish under Moyes in 2004/05, noted the Glaswegian’s growth in tactical flexibility and leadership.
Reflecting on their time together, Stubbs praised Moyes’ ability to adapt while maintaining the core values that made him successful.
Speaking on the latest episode of Goodison Park: My Home, Stubbs told the Liverpool Echo: “David’s come in and he’s talked talk about hard work, teamwork, being hard to beat, resilience, all these things.
“You could see that he had the bit between his teeth. He was a young manager, very enthusiastic, very keen to prove to people that he’s good enough for this role.
“He was prepared to take anybody on in the early days and as I think he’d come from Preston where he was a very dominant figure. He comes to Everton and we had some big personalities in that dressing room, so for a manager to come in, it probably wasn’t the easiest dressing room.
“Not in a bad way, but in terms of big personalities and trying to dominate them, I would say his biggest task was to get those people onside. I think early on he was he was not forgiving, it was ‘my way or the highway – if you don’t like it, off you go’.
“I think we were like, ‘okay’. Not in a bad way, but like thinking, okay, this is going to be interesting.
“To be fair to him, I think he realised quite quickly that he had to choose his battles very carefully. Over the years at Everton, he certainly evolved as a manager.
“Certainly when I was there, from the time that he, came to when he left, he, took the club, I think, to a real, real good place. He grew the team, he grew the club.
“We were consistently more often than not towards the end becoming a top six, seven, eight team. We were always around those places, which seems when you look back now like a relative golden age, so I definitely think people appreciated the job that David did first time around.”