Pogba was at Old Trafford to watch the 2-2 draw, which Derby won 8-7 on penalties.
The France global captained the side in the Premier League openers against Leicester and Brighton in the absence of Antonio Valencia, just as he did in last week's Champions League win at Young Boys.
Marcus Rashford is out as he serves the final game of a three-match suspension.
For the sake of the club, it would be best if Pogba and Jose go their separate ways, in an amicable manner, and United would be served well using the cash to fill the gaps in their squad.
"[Mourinho] is a manager who was hugely influential on my career twice - but particularly the first time around", added Lampard.
"Obviously, people liked what they saw in the match against Young Boys".
"I think he actually said that before the penalties, but I appreciate it".
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"The players were happy with that decision and the reasons behind the manager's decision".
Mourinho appeared to say something to him that he didn't like, which left the World Cup-winning midfielder visibly frustrated.
In extended footage, which lasted for over two minutes, Pogba appeared to be outspoken - in whatever they were discussing - before they both walked away. That if Mourinho goes you'll see a new Pogba, you won't, I can assure Manchester United fans you won't.
There was still time for United to haul themselves back level and set up a penalty shoot-out, with Marouane Fellaini once again coming to the rescue of his below-par side with a trademark header of his own.
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Mourinho was far from pleased with his club-record signing and spoke to his players in the dressing room after the disappointing draw with Wolves.