Ole Gunnar Solskjaer praised Paul Pogba's character and expressed disbelief over the racism directed at the Manchester United midfielder on social media.
World Cup winner Pogba was the subject of discriminatory posts online after failing to convert a penalty in the 1-1 draw at Wolves on Monday.
United condemned the abuse and pledged to take the "strongest course of action available" ahead of a meeting between the club, Twitter and anti-discriminatory body Kick It Out.
Pogba's team-mates have spoken out in support of the France international in recent days while advocating for stricter identification protocols for social media users.
"Paul's fine, Paul's a strong character and it makes him stronger," Solskjaer said, speaking ahead of Saturday's match against Crystal Palace.
"When you speak to him he's fine and I just cannot be believe we're still sitting here in 2019 talking about these instances.
"Social media is a place where people can hide behind fake identifies. It's not down to me to change it but there are so many Ole Gunnar Solskjaers on Twitter, and I know it's not me.
"We've got to do something about it and the authorities have got to do something about it.
"You feel sorry for [the social media trolls], they must have problems themselves."
Solskjaer added: "We need to protect individuals and protect people. When there are death threats and racism, it's serious allegations, serious incidents.
"Sometimes you get annoyed, what can we do about it as Manchester United? We're not going to ban our players from using social media. We have to spread the good word instead.
"We can use it to spread good and have to stop those incidents."
Pogba's role as penalty taker at Molineux raised eyebrows, as Marcus Rashford had successfully converted a spot-kick in the 4-0 win over Chelsea on the opening weekend.
Solskjaer confirmed the pair would continue to share the responsibility but denied the players were left to their own devices when making decisions.
"It's not that I've left it to the players, we've nominated two and throughout the season you'll have games where they are not playing and it's good to know they're there and trusted to take penalties," the Red Devils boss said.
"It's not like anarchy and they can do whatever they want, we have a few, last year we had Marcus, Jesse [Lingard] and Paul.
"It's not left to them."