The World Cup-winning midfielder was benched in midweek for a crunch Premier League clash with Arsenal.
Romelu Lukaku was also named among the substitutes after failing to deliver an attacking spark.
Giggs did not expect the Belgian striker to slip out of the United side, but he admits much more is expected of £89 million man Pogba during another testing campaign.
“Jose went with the speed of Anthony Martial, Jesse Lingard and Marcus Rashford, which you can understand as well.
“Pogba just didn't play well at Southampton so I can understand that one. He could come back in quite easily and make an impact on Saturday [against Fulham].
“He needs to really because he's taking a lot of criticism, which I think comes because of what he is capable of. Especially as a midfielder at United, you need to be consistently good and he has just shown glimpses really.
“We all know what he's capable of because we've seen it, he just has to do it regularly.
“It's down to Paul - every United fan was excited when we signed him because of what he is capable of and what he achieved at Juventus and with France, but he's just not done it on that consistent basis and you can see why Jose left him out.”
Mourinho will be hoping to find a winning formula against Fulham, after four league games without success, and Giggs believes a top-four finish can still be achieved by an out-of-sorts side despite United sitting eight points off that pace at present.
The Welshman added: “The top four at the moment looks a long way away, but there's a long way to go in the season and that's the plus.
“They've got to start winning if they have any ambitions of finishing in the top four and they are stuttering at the moment results-wise.
“It would be good to beat Fulham at home because we've seen that in the bigger games, okay we got beat by Tottenham, who played pretty well, and against City too, but at Chelsea we played really well, so we are going to be up for the big games. It's just these sides outside the top six where we've stuttered.
“It is not going to be easy against Fulham because Claudio Ranieri's just taken over there, but they are bottom and if you have any top four aspirations you've got to win these games.”