Mourinho was sacked by United in December 2018 before he was appointed at Spurs in November 2019 and again dismissed in April. He was announced as Roma's new manager in May.
At United, Mourinho won the Community Shield, EFL Cup and Europa League while he led Spurs to the EFL Cup final, but he was dismissed before the showpiece took place, which Tottenham lost 1-0 to Manchester City.
"I won three trophies at Manchester United and that was seen as a disaster," Mourinho said. "I reached a cup final which I was not allowed to play at Tottenham, and that was seen as a disaster.
"What's a disaster for me is considered a great success for others."
Prior to taking over at United in 2017, Mourinho was considered one of the best managers in the game, having led unfancied FC Porto to Champions League success before winning back-to-back Premier League titles with Chelsea -- their first in 50 years -- as well as the EFL Cup twice and an FA Cup.
He then won a Serie A, Coppa Italia and Champions League Treble with Inter Milan, and a Copa del Rey and La Liga title with Real Madrid before he returned to Chelsea and won the Premier League and EFL Cup again.
Asked whether his spells at United and Tottenham had harmed his reputation, Mourinho said: "I have nothing to say. In my last three clubs I won the title at Chelsea, three cups at United, a final at Tottenham, we arrived sixth, reaching the Europa League. What's considered a disaster for me it's something that others have never achieved, it's my fault."
Mourinho, who is the first managerial appointment under the new ownership of Friedkin family from the U.S., received a hugely positive reception from the Roma fans following his announcement.
"I want to thank the fans for their warm welcome, it was incredible as I still haven't done anything," he said. "I thank the club and the Friedkin family, the way I was welcomed was fantastic and I was impressed.
"I arrived here before nothing comes from nothing, and that's a very similar feeling to what I felt when I spoke to Dan [Friedkin] and Ryan [Friedkin]."