Prior to his sacking at Chelsea, Graham Potter revealed his mental health and family life had suffered as a result of the pressures of Premier League management.
West Ham's David Moyes also discussed the impact of being an under-fire Premier League boss, citing the harmful effects media scrutiny can have.
But Bevan, who has been in his role since 2008, believes the LMA is doing its bit to help top-flight managers cope with the strain.
"I think since COVID, the world of sport, not just football, has put health and wellbeing at the forefront of all decisions," Bevan said when speaking to Stats Perform at the Football Business Awards.
"Certainly, in the LMA, we have two in-house psychiatrists and two in-house psychologists.
"It's not just about the managers and coaches, it's looking after the people that work in that environment. We are very, very active in making sure that communication and the services that we offer are utilised as much by the families as well as by the coaches and the managers.
"So it's really important to be as well as physically fit, emotionally fit, and mentally fit, in order to do the jobs, whether you're a coach or working in any environment today."
There has been a record number of managerial dismissals in the Premier League this season.
One of those, Patrick Vieira's sacking by Crystal Palace in March, left the Premier League without a black manager.
Bevan explained the LMA is encouraging clubs to diversify their coaching staff.
He said: "From our perspective, it's making sure that we have a very vibrant pipeline of coaches coming through.
"We're pushing the stakeholders to have a far greater number of coaches from diverse backgrounds that have, for example, the [UEFA] Pro Licence, so that pipeline which the employers are looking at can make a difference over the next five years."
As of the final day of the 2022-23 season, 10 Premier League bosses are from overseas, while the competition has been won by a foreign manager in each of the last 10 seasons.
Bevan lauded the impact managers from other countries had brought to the English game, adding: "They all bring excellence.
"I think we're very lucky that the Premier League and, indeed, all of our leagues are immensely popular around the world, and they attract overseas owners, overseas coaches, and overseas players, so ensuring that the very best in their profession I work in our leagues is really special.
"We're really grateful that we have a really diverse mix of managers and coaches."
Arteta has been praised since taking the helm in December last year, having lost just two of 15 games in charge.
Former Arsenal captain Vieira, who was also linked to the job, hailed Arteta for his work so far at Emirates Stadium.
"When you're a Gunner, always a Gunner, so I'm watching them all the time, I watch their games," the Nice head coach told Ian Wright in an interview for Adidas.
"What is really interesting with Arteta is that he brings the energy back and it looks like they are playing for the club, but for the manager as well, and I think that is really important."
Vieira has been at the helm of Nice since 2018, and was linked with a return to Arsenal after Unai Emery was sacked last year.
The Frenchman said he wanted to manage a big club, but he is happy at Nice.
"I really don't know what the future will be, but doing this job it was like being a player," Vieira said.
"I wanted to play at a high level, I wanted to play for the national team, I wanted to go to the World Cup, I wanted to play with the best players and there is no doubt as a coach I have the same kind of ambition.
"I would want to manage a team that will have a chance to win the Champions League, to play the Champions League competition.
"But at the moment, honestly, right here at Nice I am in the perfect place, perfect place because I can fulfil my ambitions, the club is really ambitious and the club give me the tools to grow as a manager, but to be a part of a winning team and to play good competitions as well.
"The team is growing up really fast, really quick and hopefully I can get my ambitions with OGC Nice."
Mane, who has been widely linked with a move to German champions Bayern Munich after Liverpool announced the signing of Benfica attacker Darwin Nunez, scored 23 goals as the Reds won the EFL Cup and FA Cup last season.
He was also decisive as Senegal claimed their first Africa Cup of Nations title in February before leading his national team to World Cup qualification the following month.
Those exploits have led to suggestions he could compete with Real Madrid striker Karim Benzema to be named the world's best player later this year, and Arsenal legend and Crystal Palace manager Vieira thinks his wide-ranging abilities put him in contention.
"Sadio Mane is part of the new generation of attackers who knows how to do everything," Vieira told the Diambars Institute, a football academy in Senegal.
"He scores goals, he knows how to defend, he knows how to run in depth. He is a hard worker in the field.
"He is one of the modern attackers. For me, he should be considered for the Ballon d'Or.
"He is one of those great players who can win it. I saw him every weekend in the Premier League and for me, he is one of the great European strikers."
Having won six trophies in a six-year spell at Anfield, Mane is expected to move to Bayern in the current transfer window, perhaps as a replacement for Barcelona-linked striker Robert Lewandowski.
Asked about such rumours, Vieira said Mane will make the best decision for his career.
"I think he has his head on his shoulders to make the best decision," the Frenchman added.
"Should he stay or go? It's up to him to make that decision. But he is a player that I admire in relation to his talent as a footballer, but also in relation to his talent as a man."
Coaches including Jose Mourinho, Fabio Capello, Zinedine Zidane, Carlo Ancelotti, Gareth Southgate and Fabio Capello have joined the 24-man UEFA football board, along with superstar former players Paolo Maldini, Luis Figo, Gareth Bale, Rio Ferdinand, Michael Laudrup, Philipp Lahm and Robbie Keane.
There is one non-European on the board, with Inter's Argentine vice-president Javier Zanetti joining a throng that also includes former Germany team-mates Rudi Voller and Jurgen Klinsmann, plus Netherlands boss Ronald Koeman, Rafael Benitez, Patrick Vieira and Eric Abidal.
The noticeably all-male board will hold its first meeting at UEFA's European House of Football headquarters on Monday.
European football's governing body said the group will "give an institutional yet independent voice of experience and expertise on fundamental football-related topics".
UEFA president Aleksander Ceferin said: "UEFA is delighted to see that the very ones who have shaped the game's history with their talents and philosophy through decades are gathered again around our common goal – to protect the game of football and its essential values. As we always say: football first!"
Ceferin is campaigning for clarity on football's handball rules, having recently described the law as "really obscure".
"No one understands it any more," Ceferin said. "So we really need a conversation here, finding solutions and clarifying some issues."
He said that would be an issue for the football board to look at, and it was confirmed on Thursday as being on the agenda for the meeting, along with discussions about the video assistant referee system, player behaviour and medical issues.
UEFA said its technical director and chief of football Zvonimir Boban would chair Monday's meeting, although he is not a member of the new board.
UEFA football board members: Jose Mourinho (Portugal), Carlo Ancelotti (Italy), Zinedine Zidane (France), Paolo Maldini (Italy), Fabio Capello (Italy), Javier Zanetti (Argentina), Luis Figo (Portugal), Philipp Lahm (Germany), Ronald Koeman (Netherlands), Gareth Southgate (England), Rio Ferdinand (England), Michael Laudrup (Denmark), Rafael Benitez (Spain), Roberto Martinez (Spain)
Predrag Mijatovic (Montenegro), Jurgen Klinsmann (Germany), Rudi Voller (Germany), Petr Cech (Czech Republic), Juan Mata (Spain), Robbie Keane (Republic of Ireland), Patrick Vieira (France), Henrik Larsson (Sweden), Eric Abidal (France), Gareth Bale (Wales).
