The Duke of Sussex also warned of the dangers of social media, declaring it ‘more addictive than drugs and alcohol’.
The Royal father-to-be made the comments during a roundtable discussion on young people's mental health.
Harry visited the YMCA in South Ealing, west London, on Wednesday, to discuss and met with representatives from charities including Stonewall and Young Minds.
The roundtable event was convened by Heads Together, a mental health initiative headed by the Duke and Duchess of Cambridge and the Duke and Duchess of Sussex.
Harry said: ‘There's too much negativity surrounding mental health and it must be so hard for young people to talk about it.
‘Social media is more addictive than drugs and alcohol, and it's more dangerous because it's normalised and there are no restrictions to it.
‘We are in quite a mind-altering time, but quite an exciting time, because everyone in this room has the opportunity to make a real difference.’
Prince Harry also believes that Fortnite and games like it ‘shouldn’t be allowed'.
The Metro reports that he explained: ‘A game like Fornite for instance may not be so good for children.
‘Parents have got their hands up; they don’t know what to do about it.
‘Fornite shouldn’t be allowed.’
In a post to the new Sussex Instagram account, a picture of Harry during the visit was shared, and he was quoted as saying: ‘There continues to be huge progress in smashing the stigma that surrounds mental health, but let's keep normalising the conversation.
‘Let's keep reminding each other that it's okay to not be okay, and to listen to each other.
‘After all, how we think determines how we act, how we feel, and how we treat ourselves and those around us.’
YMCA South Ealing is part of the YMCA St Paul's Group, which provides services across London and is one of the largest in Europe.
The association provides housing for 150 young people who are dealing with a range of problems such as homelessness, mental illness, substance misuse and domestic violence.
Earlier in the afternoon, Harry spoke with three residents at the YMCA, Jade Messa-Goodenough, Julie Spencer and Rory Tomlinson.
He told them: ‘One of the most comforting things to know is you're not alone and you're one of the more as opposed to one of the few.
‘Your own experience is very unique to you but the relatability of people in this place and everybody outside is huge. It's hugely relatable, even more so today than it was four years ago.’
Elsewhere during the tour he discussed the #IAmWhole campaign with young champions for mental health.
The campaign, developed by the NHS and YMCA, encourages young people to speak openly about their mental health issues.
Harry finished with a ballet demonstration by a group of children between the ages of four and six, during which he tested his balance in a short exercise.