England full-back Johnson served under Mourinho at Chelsea, but he was never able to become a regular first-team player at Stamford Bridge.
Johnson feels that the Portuguese tactician was unable to get the best out of him and says that Liverpool boss Rodgers is better at 'man management'.
"It was difficult for me under Jose at Chelsea because there was a moment when he said I deserved to play on merit," he told the Daily Mail.
"He said if I played well in the next game I would play the week after. I got man of the match so he couldn't drop me. Then in the next game he said the same thing and I got man of the match again.
"Then we had another game and after that Barcelona. I remember speaking to my agent and saying, 'He won't play me in this game because if I play well then he has to play me against Barcelona', and I knew that wasn't going to happen.
"He didn't play me in that game and from that moment I just lost it and thought, 'Well, how am I meant to respect you now? It's just finished'.
"Brendan wouldn't do that. He's shown that if you're good enough you're old enough and you'll play in the big games if you deserve to. So in terms of man management, Brendan is definitely better."
Johnson believes Rodgers' style of play is not easily copied, adding: "Some managers like the thought of playing the way Brendan does but haven't got the confidence or knowhow to pull it off.
"Others would probably have panicked and changed their philosophy just to try and win. But Brendan was mentally strong enough and knew what he was trying to implement was right and that once we grabbed hold of it we would be a success."
Liverpool have moved to second in the table, just four points off leaders Chelsea, and Johnson admits their confidence could not be higher.
"We believe we can win every game and I remember having that feeling at Chelsea," he admitted.
"The first year we won the title (2005) we could be losing 2-0 and still think we would win, and we usually would. That was confidence at its peak and we are moving towards that at Liverpool.
"You have to believe you can win the league and until there are not enough points available we'll keep thinking we can. We've got 10 cup finals, really, because we can't afford to lose games or drop many points because Manchester City and Chelsea won't.
"City are favourites because they could field a second team that would be competitive, and you can't compete with that. So we will need a bit of luck but we are definitely good enough.
"Our goal at the start of the season was to finish in the top four and that is still our minimum aim. Finishing third, second or winning the title is a bonus but we are in a good position.
"The character and mentality in this squad are different. There were games last season when we battered teams and didn't get results. We've got more of a killer instinct this year."
Johnson, who is set to win his 50th cap for England against Denmark on Wednesday, insists that he has nothing to prove.
"I know I could have had a better season, but you can't play 12 years in the Premier League and not have a bad couple of weeks," he said.
"I'm my biggest critic and I don't need to be told when I'm playing badly.
"You don't get 49 England caps, play in World Cups and European Championships, you don't win the Premier League twice, the League Cup twice and the FA Cup if you can't defend. It's that simple.
"No disrespect, but you'd be in the Championship."