The England right back says he lost respect for the Portuguese manager after he was dropped from the Blues' lineup despite putting in a man-of-the-match performance.
The England international, who played under the Portuguese between 2004 and 2006, said he could not trust the former Porto coach to keep his word.
"It was difficult for me under Jose at Chelsea because there was a moment when he said I deserved to play on merit," the right back 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 does not doubt Mourinho's quality but has hailed Rodgers' style and proclaimed the Northern Irishman one of the best coaches around.
"Mourinho is one of the best in the world and I would never say he’s not because of what happened between us," he added. "But Brendan is different to Jose, he has his own mentality and is definitely one of the best.
"Some managers like the thought of playing the way Brendan does but haven't got the confidence or know how to pull it off. Others would probably have panicked and changed their philosophy just to try to 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 currently sits second in the Premier League table, four points behind Chelsea, and Johnson believes improved mental strength has been the difference for Rodgers' men this season.
"In previous seasons, when Stoke (in January) pegged us back to 2-2, people would have crumbled or not felt relaxed enough to play their own game and we might have drawn or even lost," he continued. "So to score five and get three points at a ground where we hadn't won in the Premier League was a big statement. We are a different side now."