Henderson was handed his second Premier League start of the season against his former club in place of David De Gea. It was his error that led to David McGoldrick giving Sheffield United the lead but the 23-year-old England goalkeeper made amends with a wonder save from Rhian Brewster to deny the home side a late equaliser.
"It was the good, bad and the ugly, maybe in a different order," said Solskjaer when asked to assess Henderson's performance. "He is always learning. He has probably been looking forward to coming back here and to get from that start shows his character for the rest of the game."
After Henderson's early mistake, Marcus Rashford's double and Anthony Martial's first league goal of the season made it 3-1 before McGoldrick's second of the game made for a nervous finish for Solskjaer's team, who have won all six away games this season despite conceding first each time.
"I thought all three goals were excellent," said Solskjaer. "I wanted to test them here today, we knew it was going to be a physical test. The fight, we are going to get kicked. It is one of these games the boys will learn from.
"We need to sort the home form. It is not like it is home and away with these conditions without fans. We should be more used to the Old Trafford pitches than these pitches. Sunday [against Leeds United] is a massive game, we have been waiting for years and we will be ready for it."