Per Sky Sports' Gerard Brand, Solskjaer spoke about the midfielder's superb recent form:
"I've not released those [qualities], he is playing to his potential, we are trying to put this team forward to put players in positions to where we can hurt teams.
"We know Paul can do that with his physicality, energy, strength into the box, is going to cause problems. I speak to him like I do with the others, it's about getting the best out of players, that's management.
"He's responding to the way we do things now, onto the next one."
Pogba gave United the lead in the 14th minute at Craven Cottage when he lashed home a through ball from Anthony Martial, who doubled their tally with a goal of his own nine minutes later.
The 25-year-old midfielder capped an excellent showing with a second goal midway through the second half. After Maxime Le Marchand fouled Juan Mata in the box, Pogba stepped up to dispatch the resulting penalty.
The Manchester Evening News shared further praise for Pogba from Solskjaer:
Football analyst Dave O'Brien shared his numbers from the match:
Though Solskjaer may not have taken all the credit for Pogba's form, the Norwegian's arrival at Old Trafford has had a transformative effect on him.
In nine Premier League appearances under the former Red Devils striker, Pogba has returned eight goals and five assists. Under predecessor Jose Mourinho, he had contributed just three of each in 14 league games.
Sky Sports Statto shared further evidence that Pogba has reached a new level of productivity:
Under Mourinho, Pogba struggled to show more than the occasional flash of his brilliance.
However, he has much more freedom to operate under the more attack-minded Solskjaer, and that forward-thinking approach gives him the licence to get up the pitch, create chances and get on the receiving end of them.
United take on Paris Saint-Germain on Tuesday in the first leg of their UEFA Champions League last-16 tie, and with Pogba increasingly having a decisive influence in their games, the Red Devils have a much better chance of progressing than they did when the draw was made in December.