The Gunners went down with little fight as the Seagulls earned a third successive win on the trot at the Emirates Stadium, a result which means Manchester City can retain their title with a win over Chelsea next Sunday.
Arsenal have faced accusations of "bottling" the title, having lead the table for longer than any other team in Premier League history, and Keane believes the back-to-back draws with West Ham and Southampton sealed the Gunners' fate.
"When you look at some of the games of the past five or six weeks, particularly the West Ham and Southampton games stand out," he told Sky Sports.
"I know they dropped points when losing at Manchester City, and drawing with Liverpool, which can happen. You can't win every game, they've won 25 league games which is fantastic. But the points they lost against West Ham and Southampton definitely knocked them back a bit.
"We saw a team today which was physically and mentally shot. It really was. As soon as Brighton started flexing their muscles, passing and moving, looking really sharper and quicker.”
Keane also believes that Arsenal’s lack squad depth has played a huge role, insisting Mikel Arteta needs to sign four or five more players in the summer to mount another title race.
"We have said [all season] that if they had a few injuries, then Arsenal would struggle. Arsenal don't have the strength and depth of Manchester City, the experience, the better quality in terms of their squad.
"They have come up short, they need four or five players. It's easy to say that, but it's the right player and the right character.
"So if they get in this position again, pole position, and they have one or two injuries, then they need quality to come in. We saw with City today [bringing on Jack Grealish], but when Arsenal make changes, it weakens the team."