Rangnick's decision to substitute Pogba in the second half of the 3-2 win over Norwich on Saturday was initially greeted with cheers by supporters before they turned to boos as he walked off. There were chants of "f--- off Pogba".
The 29-year-old was given another hostile reception at the final whistle as he appeared to cup his ear in the direction of the Stretford End.
"I didn't hear it myself to be honest, we were talking about it with my staff in the locker room," Rangnick said when asked about the response from the fans towards Pogba.
"I think the fans here are amazing, I really do. The support in the stadium today was great, it could not have been any better.
"I can understand if the fans are frustrated and disappointed, so are we. I don't think it makes sense to take on and to target any individual person or player. It's a collective responsibility. For me it doesn't make sense and this is why I will always defend and protect my players.
"By the way I think Paul in the first half in possession of the ball did well."
Thousands of United fans marched in protest against the club's owners ahead the match, before the players were targeted as Norwich came from 2-0 down to level at 2-2, with chants of "you're not fit to wear the shirt" coming down from the terraces.
Rangnick was also asked in his post-match news conference about the video circulating on social media of Pogba, who is out of contract in the summer, cupping his ear as he walked down the tunnel at full-time.
"I didn't see it, I heard that," he added. "It was probably his reaction to the chanting of the fans. As I said, I can understand in a way the fans and supporters but it doesn't make sense to take on individual players."
Regarding the pre-match fan protests, a United spokesperson released a statement that read: "We are working hard to create the conditions for renewed success on the pitch, while strengthening our engagement with fans.
"We respect the right of fans to voice their opinions peacefully and we will continue to listen to them, with the aim of working together to get the club back to where we all want it to be: competing for trophies."
As far as for the match itself, United had Cristiano Ronaldo to thank for their narrow victory over bottom side Norwich after the 37-year-old netted his 50th career hat-trick.
The result means Rangnick's team are three points closer to the top four after defeats for both Tottenham and Arsenal but the interim coach was not bullish about their chances of qualifying for next season's Champions League with trips to Liverpool and Arsenal to come next week.
"Everybody has seen today's game, we all know what team we're playing on Tuesday," Rangnick said.
"They might have the chance to win four trophies. If we play like we played today it will be very, very difficult to get even a point out of this game; this is what we have to be realistically aware of.
"We need to raise our own level and standard. We have to be realistic, we have to play a lot better if Liverpool are in possession of the ball than we did today."