A panel featuring Fabio Capello, Jurgen Klinsmann, Ronald Koeman, Luis Figo and Zinedine Zidane made a range of recommendations after its inaugural meeting in Nyon, Switzerland.
The group also called for referees to get tougher with diving players by being "more decisive" in dealing with those who attempt to gain free-kicks or penalties through con tricks.
UEFA, which is European football's governing body, said discussions were "engaging and constructive" as the elite board considered the Laws of the Game, which are set by the International Football Association Board (IFAB).
Also attending were the likes of Rafael Benitez, Petr Cech, Philipp Lahm, Michael Laudrup, Javier Zanetti, Patrick Vieira, Gareth Southgate and Rudi Voller.
UEFA was urged by the board to clarify that handball should not be called if the ball deflects off a player's body and onto their arm or hand, especially when the ball does not go towards goal.
It was also recommended that handball following a shot at goal should not automatically be punished by a caution.
The newly formed board met at UEFA's headquarters and said the European confederation should make the case to IFAB that its rules are too clear-cut regarding red cards for handballs that prevent a goal.
In a statement, UEFA said that when it comes to such a situation, the board "feels players should be sent off only if they deliberately and intentionally touch the ball with their hand/arm" and in other circumstances a yellow card should suffice.
UEFA chief of football Zvonimir Boban said: "Having such beautiful football minds around the same table proved to be not just desirable but necessary.
"It was a true honour to be part of such an open and genuine discussion, and I am confident that we have found reasonable solutions to overcome a few stumbling blocks that negatively impact what happens on the field of play.
"It might sound like a banality, but mistakes happen, and we should not stigmatise them, influenced by the shirt we wear. The handball rule, for example, will always be disputed, but we can make it more consistent and aligned with the game's true nature."
The six-time Ballon d'Or winner stunned the world in August when he informed Barca of his intention to leave the club he has spent two decades with.
He intended to trigger a clause in his contract to walk away on a free transfer, but the validity of such a stipulation was made murky due to last season being prolonged into August by the coronavirus pandemic.
But Figo, who made a surprising and controversial move from Barca to bitter rivals Real Madrid in 2000, believes Messi will now have his mind set on departing Catalonia.
"I watched the thing with Messi and his attempt to leave Barcelona this summer like all football fans: expectantly and surprised," he told Marca.
"He'll have his motives and reasons for making that decision. I don't know what happened beforehand.
"Every club wants a player like Messi, but then it depends on factors like the current financial situation at the club, the money he'll cost the club in wages, the will of the player...
"But generally, in life, if you don't want to be somewhere, in the end there's nothing that can change your mind."
Messi, who is due to become a free agent at the end of the campaign, has endured an underwhelming start to the 2020-21 season.
The 33-year-old had failed to assist a goal or score from open play in six LaLiga matches before last weekend's 5-2 win over Real Betis, when he also netted from the penalty spot.
He started that game on the bench - the first time that has happened in the league since September 2019 - but Ronald Koeman has since revealed Messi was carrying a knock.
Messi is now on international duty with Argentina and played the full 90 minutes of Thursday's 1-1 World Cup qualifying draw with Paraguay, the forward having a goal ruled out by VAR in that game.
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).
