Jose Mourinho benched the Frenchman for Manchester United's Champions League first leg against Sevilla on Wednesday night after he missed Saturday's win over Huddersfield through illness.
Despite the scrutiny on Pogba's form, Keane suggested other United players were hiding behind the former Juventus star's 'big personality'.
"[Paul] Pogba is a really good player," Keane told ITV Sport.
"He is under a lot of pressure at the moment, there is a lot of speculation about him, he was left out tonight, but you'd still have him in your starting XI.
"Off the field, he has a big personality with the social media, his haircuts, the cars he drives, he needs to bring that on the pitch.
"But United's problems aren't just with Pogba. Lukaku needs to do more, Sanchez has got to do better, they need to reinvest in some defenders.
"You can't keep pointing the finger at Pogba, but the lad has got to do better."
Keane also suggested Manchester United are still short of two or three players as they continue to re-build following the reigns of Louis van Gaal and David Moyes.
"To me they're still rebuilding and they're still two or three players short, so their short-term targets at the moment are to get through these ties without playing that well.
"If you're a player or a coach you'll be going back on the plane tonight going 'Listen lads, we didn't play great, but job done, we got a decent result and we expect to get through the second leg.'"
Speaking after the game Mourinho decided to focus on the performance of Scott McTominay, before briefly touching on Pogba's appearance as a substitute.
“In my pre-match interview, in four questions I had three about Paul, and Paul was not even playing,” Mourinho told BT Sport journalist, Des Kelly.
“Respecting you and your work, I understand your question. But if I was one of you, I would ask if the Manchester United manager agrees that Scott McTominay had a fantastic performance, and my answer would be yes, he had a fantastic performance.
“He looked a senior player, a player with great maturity, with tactical sense, with a sense of responsibility, good in possession, good in pressing. He looked like a man with dozens and dozens of matches in the Champions League when this is only the second one.
“Paul tried to give the team what I asked. Of course he lost a couple of possessions, but he also gave us stability, because we had a good percentage of ball possession away from home against a good team like Sevilla.”