Pogba scored twice in United's 3-0 win at Craven Cottage; fellow Parisian Anthony Martial got the other with a superb solo effort.
Following the Champions League round-of-16 first leg, United visit Chelsea in the FA Cup before a clash against Liverpool in the Premier League.
Ranieri understands the frustration of the fans, many of whom chanted "You don't know what you're doing" when Ranieri took off Andre Schurrle for Cyrus Christie after 53 minutes.
But that confident play was short-lived, with an early error by Fulham centre-back Maxime Le Marchand sapping confidence.
"He's been a threat in the first 20 minutes like you wouldn't believe".
So concerned about Martial cutting onto his right foot, Fulham failed to properly track Pogba's run and the midfielder lashed home from an acute angle.
Fulham fans made their feelings clear as they booed Schurrle when he was replaced by Cyrus Christie on 53 minutes and applauded the decision to take off Ryan Babel on 77 minutes after the Netherlands worldwide had hit the post from point blank range.
United won possession and Phil Jones found the fleet-footed attacker just inside his own half. "I told my players that it's important to show our fans we're alive, we try to do our best until the end".
The hosts, who started the day seven points from safety, looked unlikely to mount any sort of comeback - and the game was put to bed as a contest on 65 minutes when Pogba scored his second from penalty spot after Juan Mata had been fouled in the box.
The visitors were now in complete control against a Fulham side looking more and more likely to find themselves playing Championship football next season.
Solskjaer says he spoke to co-owner Avram Glazer after the match when the American visited the United dressing room, but he insists the team's improvement is not simply down to his impact.