Spurs took the lead at Vicarge Road, only for two quick-fire goals to condemn them to a shock defeat.
The loss was Mauricio Pochettino's side's first defeat of the campaign, despite the Argentine warning against complacency after the impressive victory over Manchester United last week.
"He will be annoyed," Souness told 'Sky Sports'. "Because he has warned them and some of them have not heeded the warning, I can't remember him being that annoyed [as he was in his post-match interview].
"For a large part of the second half Watford were better than Tottenham. The fact they got the goals from set-pieces isn't good for Spurs, but I would be more worried about some players not competing in the second half when the going got really tough and some of them got rolled over.
"If you are going to be one of the big teams, a contender, then you fear nobody. This might be a punch on the nose, maybe a wake-up call for them to go again. If you are a big team and a big player this is when you turn up.
"Everyone can be a big personality in the dressing room when you are winning, but it's when you have a punch on the nose like this that it finds out if you are a proper team. Can you brush the criticism away and deal with the disappointment? If it's the biggest game of the season or one of the less-fancied teams you do what you have to do to get back on track."
The Scot insisted that Spurs' leaders need to stand up, particularly with a tricky clash with Liverpool awaiting them after the international break.
"If you have one leader in your team you have a chance, if you have two you might be winning things, if you have three you are near enough guaranteed to win things," he said.
"They are so hard to find and are the difference between very good players and the ones who can drag the lesser lights through difficult times. That's what Tottenham need right now, they need some men who can shrug this off and make the difference when they play Liverpool."