Adkins was dismissed by Saints chairman Nicola Cortese despite a run of just two defeats in 12 matches and McDermott believes that the former Scunthorpe United manager deserved more respect in the wake of his sacking.
McDermott told reporters: "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 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."