The 32-year-old reiterated his commitment to encouraging people to speak out and seek help for their mental health problems.
And he suggested that young people constantly checking their mobile phones was an example of how everyone would benefit from taking "a moment to process our thoughts rather than rushing from one thing to the next".
Harry was speaking at an event in Leeds aimed at highlighting issues affecting the mental well-being of young people in the city and how organisations are helping.
Royal visit: News, pictures and reaction as Prince Harry comes to LeedsHe said: "But what has struck me most is the number of people I've met who have direct experience of mental health challenges, either themselves or those close to them.
"So many of these stories could have been very different if awareness was better and help had been sought sooner.
"I cannot tell you how pleased William, Catherine and I are that the dial seems to have shifted and that there is now greater understanding, compassion and kindness for anyone who opens up about their struggles.
"But let's not kid ourselves that the job is done - there is much, much more that we can do at every level to make conversations about mental health as commonplace as those about physical health."
The Prince added: "For example, we need to better equip our young people with the tools they need to cope with this increasingly complex and fast-moving world we live in.
"I read recently that young people check their phones at least 150 times per day - I'm sure we could all be more effective and efficient if we took a moment to process our thoughts rather than rushing from one thing to the next."
Harry was speaking at the start of a panel discussion at the Leeds Leads: Encouraging Happy Young Minds event, which brought together a range of groups focused on the mental well-being of young people in the city.
The Prince has been praised for talking about his own mental health issues and, together with the Duke and Duchess of Cambridge, highlighting the problem through their Heads Together initiative.
He said: "This year there has been a lot spoken about mental health, not just by the Heads Together campaign but by many other organisations and initiatives focused on mental health.
"The many voices that we've heard from across the country have helped to normalise the discussion about mental health, taking it away from a presumption of mental illness to a broad ranging and, most significantly, positive conversation."
The event in the Leeds was the first of a series as Harry began a two-day visit to the city.