The Tottenham boss is unhappy that Manchester City star Raheem Sterling pulled out of the latest Three Lions squad but is fit to face Spurs today.
It comes after Eric Dier got injured during last month’s international break, missing matches against West Ham in the Premier League and LASK in the Europa.
Mourinho, who said he was “okay” with Southgate playing Harry Kane against Iceland, said: “The only problem for me is it should be the same for everybody, not just for some.
“Gareth Southgate I read, supposedly told that some club managers put pressure on the players not to play for the national team.
“And because of that he feels sometimes the need to call club managers to cool down the emotions and control a difficult situation for him.
“I would like him to say who. I would like him to say which are the coaches who put pressure on the players not to go.
“And I would like him to say which are the coaches that he speaks on the phone with. He has the right, the power to call the players he wants.
“He wants to win matches, especially after a defeat the next match, even being a dead rubber, is an important match. I sympathise totally with that.
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
“Of course we all know that Sterling is going to play. When Eric Dier left the national team injured in the past month, he didn’t play two matches for Tottenham.
“He needed a couple of weeks to recover. And Raheem is going to play in this match. These are the little details that I think Gareth should explain to us all.”
Mourinho, who celebrates a year at Spurs this week, reckons his side are a different animal to the one City brushed aside 2-0 in February.
Tottenham go into the game five points ahead of Pep Guardiola’s side, with one eye on a title charge.
Mourinho said: “We are a better team. More confident. A different identity. We have more solutions.
“And in my case now, I can say that after one year, I am even happier than when I was when I got the job, so that for me is a very good feeling.
“If you ask me now: ‘Do you see yourself here in one year’s time?’ Of course I do because I’m very happy here.”
Tottenham (4-3-3) vs Man City:Lloris; Aurier, Alderweireld, Dier, Reguilon; Sissoko, Hojbjerg, Ndombele; Son, Kane, Bale