Garcia was disqualified last week for damaging five greens in the third round.
No TV footage of those incidents was available but the 2017 Masters champion was filmed thrashing around in a bunker like a petulant teenager during round two.
“I’ve been a big fan of Sergio for the last 20 years,” Jacklin told the Daily Express.
“He’s an incredibly talented golfer and I don’t know anyone in the game, including Tiger Woods, who has more ability but unfortunately he made a fool of himself last week.
“It was worthy of more than disqualification. I’d have banned him. Damaging greens on a golf course is an offence that deserves a suspension.
The European Tour have said the incident is over and it’s time to move on. Well, if he’s not going to be banned, then I’d like to see him take a self-imposed break from the game.
“I think he needs time to realise how fortunate he is, at 39, to have everything money can buy, a young family and everything to be grateful for,” said Jacklin, the most successful captain in European Ryder Cup history and winner of the 1969 Open and 1970 US Open.
“To see his frustration spill over the way it did last week shows he’s not in a well-balanced state of mind. There seems to be an anger within him and golf is a game you can’t play angry.
“You can’t start hacking away at the course. It’s wrong from every single angle. If you are a golfer in the same group as Sergio when he’s doing that, it’s not something you want to be dealing with.”
Garcia has had a long and stellar career. He is Europe’s all-time leading Ryder Cup points scorer and has won almost 40 tournaments around the world, but he also has a history of falling foul of authority.
He threw a golf shoe in a fit of pique during a tournament at Wentworth in 1999, spat in a hole at Doral in 2007 and racially insulted Tiger Woods at a dinner in 2013.
“Seeing someone go off the way he did in Saudi is embarrassing,” said Jacklin.
“There’s a code of conduct he’s overstepped. It’s unacceptable. The shame of it, having to apologise to your fellow pros.
“All golfers get frustrated from time to time. Golf can drive you crazy if you are looking for perfection because that is something you can never truly attain in this game.
“Compare Sergio with his late, great fellow Spaniard Seve Ballesteros for example. Seve had more courage than anyone.
“He was the best example of someone pulling victory out of defeat because of his raw courage and tenacity. We haven’t seen that so much from Sergio.”