McClaren rebuilt his reputation in the Netherlands by winning the Eredivisie with FC Twente following his failed tenure as England boss from 2006 to 2007.
The former Middlesbrough manager also had a less successful spell as Wolfsburg manager three years ago.
He is now enjoying a superb start to his reign as Derby boss having won 10 of 14 league matches since taking over in late September.
Mourinho, who shot to prominence by leading Porto to the Champions League in 2004, has enjoyed great success working abroad, including during his first spell as Chelsea boss from 2004 to 2007, during which he won two Premier League titles, the FA Cup and two League Cups.
"I disagree with so many foreign coaches in this country," said Mourinho. "I don't see a reason for that because I don't see the English managers are at any point behind the foreign ones.
"Influence from abroad is good, you can learn from other cultures, but I think the main culture has to always be the English, in this case the British, culture.
"But I think if there are no jobs in the country as a manager or as a player you have to go, because this is a short professional life. So go and enjoy. You have always the chance to come back.
"In this country, people shouldn't be afraid to be a bit adventurous, like other coaches from other nationalities.
"Football is the same everywhere: 11 against 11, one ball, two goals.
"To go abroad is a fantastic experience and sometimes it looks like English players, English managers, they don't like to go abroad.
"What is happening now is that they don't go abroad but others are coming to their country."
To many in this country, McClaren is still chiefly associated with England's failure to qualify for Euro 2008 under his tenure. However, Mourinho feels more respect should be given to him for his success in the Netherlands.
"I almost forgot that he was England manager. It was a period which ended. He moved on," added Mourinho.
"The first thing that comes to my memory if you ask me about Steve, it's not being the England manager. It's being champion in Holland. He did well.
"I spoke with him to say congratulations to him when he was champion in Holland, an important moment of his career after such a difficult part of it.
"Of course he suffered but he moved on. He went to Holland, he went to Germany. New cultures, new football."