Pogba was penalised for handling the ball in the penalty area in first half stoppage time, allowing Michail Antonio to open the scoring from the spot.
Mason Greenwood equalised in the second half to earn a 1-1 draw and leave United needing a point against Leicester on Sunday to qualify for the Champions League but Solskjaer insisted afterwards that Pogba knows he should have let Rice's free kick hit him in the face.
"It's a natural reaction," Solskjaer said.
"Paul held hands up knowing he should have taken it in the mush. It came flying at him at 100 miles an hour."
The draw means United go into their head-to-head with Leicester on the final day of the season a point ahead of Brendan Rodgers' side and if they avoid defeat at the King Power Stadium, they will secure a top-four finish for the first time since 2018.
"After lockdown we had to go for it, we had to go for goal difference and points and the effort has been fantastic," Solskjaer said.
"We've given ourselves a fantastic opportunity and a great starting point for Sunday."
As well as heaping praise on goalscorer Greenwood, who got his 10th Premier League goal of the season, Solskjaer also highlighted David de Gea's performance after the Spaniard bounced back from his dismal display against Chelsea to make a crucial save from Jarrod Bowen to keep the score at 1-1.
"David showed why we keep him in that goal, it was a great save," Solskjaer said.
"I knew he was going to be focused. Everyone is hurt by what happened on Sunday but he has shown today he can keep his concentration."