The Ivory Coast attacker played under Mourinho during two spells at Stamford Bridge, winning four Premier League titles and four FA Cups.
And Drogba insisted the Manchester United boss would have won the Premier League if he was in charge of their neighbours.
"I think if you put him at Manchester City, he would have won the league twice, maybe two or three times," said Drogba, who officially retired from football on Wednesday.
"You get criticism because you set a standard of winning, winning and winning and now you're not winning or having the same results.
"He is still there. You have to look at all the managers who were at Manchester United the last few years."
Drogba, who admitted Mourinho had to convince him to stay at Chelsea after a difficult first season, believes Mourinho has had a tough time at Manchester United and deserves more time to effect change at Old Trafford.
The Portuguese has yet to win the league with the Red Devils.
But has lifted the Europa League and FA Cup in his two-and-a-half years in Manchester.
"Being manager after Sir Alex Ferguson is not easy and the finances that they had then are not the same as what they have now.
"People only pay attention to the best and he's one of the best and that's why he gets all of this.
"I think he's taking the challenge, because it's a big challenge and if people criticise you then how can you enjoy it? It's tough. After all, he's human.
"He's trying to change his approach and that's what the best managers do and when things are not working you try to change it."
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