Manchester UnitedPogba, 24, rejoined last summer for a world-record £89million transfer fee, having left to play for Juventus in 2012 on a free transfer.
The France international played more games than any of his United team-mates this season and he scored nine goals, including the opener in the 2-0 win over Ajax in the Europa League final.
But his hefty price tag and strong performances for Juve and France in last summer's European Championships have led some pundits to criticise his first season back in England.
Robson, however, is not one of them and he believes Pogba will eventually take over the Red Devils armband.
The former England and United skipper said of Pogba: "I think he's improved us. When he's been missing we've missed something.
Paul Pogba tipped to become future Manchester United captain
Paul Pogba tipped to become Manchester United captain
"He maybe dwells on (the ball) a bit too long for a central midfielder sometimes – you want to move it quicker.
"But Paul has got real ability and he can see a pass that splits defences. When he's not in the team, we don't have that.
"I think if Paul starts improving his performances, he could be a captain for United who leads by example."
United finished the Premier League season in sixth place, 24 points behind champions Chelsea, but Robson is adamant the campaign was a success.
Jose Mourinho guided United to three trophies and qualification for next season's Champions League, something they failed to achieve in 2015/16.
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Paul Pogba scored nine goals in first season back at Old Trafford Paul Pogba makes pilgrimage to Mecca Mon, May 29, 2017
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Man Utd star Paul Pogba has made a pilgrimage to Mecca
"People dismiss the Community Shield but as a player you always wanted to win it because it gives you confidence going into the season," he added.
"And the EFL Cup was a good win – Southampton gave us a really good game in the final.
"Now, if that had been it, you'd say it's been an OK season. But to go and win the Europa League and qualify for the Champions League you've got to say it's a very good season, especially when you consider the way the team were going.
"OK, we won the FA Cup (under Louis van Gaal) but we weren't playing the football the fans wanted to see and the squad was a little bit weak.
"(Mourinho's) four signings improved the squad (last summer), so you've got to say it's a very good season."