Pogba was an anonymous figure as his Red Devils succumbed to an embarrassing home defeat by the Premier League's basement side and was whipped off by Jose Mourinho before the hour mark.
Henry told Sky Sports: "As soon as the game started, something was weird — the atmosphere of the stadium, the team — it's so weird from what we saw from that team a week ago.
"The commitment, the desire, and I asked if Pogba can do that all the time, the way he played against City.
"The answer is nope."
He continued: "[Mourinho] was trying to calm the players down and he has experience. He saw that result way before we saw it. He had a feeling that he needed to speak to the players during the week.
"He told them be careful it is going to be different against West Brom and I go back to Pogba: why didn't you and the rest of the team do what you did against City all season?
"West Brom outworked them; they wanted to go out and hurt them. After 10 minutes, I turned and there was a weird atmosphere and I could only see West Brom scoring."