Having also taken his team up to the top flight last summer, McDermott knows how difficult managing a newly-promoted side can be.
The Royals boss, like Adkins, endured a tricky start to the season, but as has been the case with Saints, Reading have now seemingly turned a corner following an improvement in form.
McDermott has been thankful that the Reading owner Anton Zingarevich has kept faith with him through the club's rocky period and poured scorn on Cortese's treatment of Adkins, whose name was absent from Southampton's matchday programme for Pochettino's first game in charge against Everton.
''What I thought was sad was what Nigel Adkins has done for Southampton wasn't even mentioned in that programme at the Everton game. Let's have a bit of respect. That's not right,'' the Reading manager said.
''That's not right and proper. What he has done for that club has been phenomenal.
''What I find fascinating about owners is that managers who lose games start to learn. They pick up a few points. Then they are sacked. It doesn't make any sense to me.
''For me, you learn from experience. Nigel struggled at the start of the season. Then he loses two games in 12 and gets the sack.
''It doesn't seem like the right thing to do.''
McDermott has grown close to Adkins over the last few years and he hopes the former Scunthorpe boss gets another shot at the big time soon.
''Nigel has earned the right to do so,'' McDermott added.
''No one can pick and choose their jobs in management - but he has been a fantastic manager at Scunthorpe and Southampton.''