City go to Liverpool on Sunday on the back of five consecutive defeats and blowing a 3-0 lead to draw 3-3 at home to Feyenoord in the Champions League.
Souness says it's now down to the players and not manager Pep Guardiola to find a way out of their spiral.
He wrote for the Daily Mail: "The stress of managing Manchester City lately was etched all over Pep Guardiola's face following their midweek capitulation against Feyenoord.
"After all, this is a new experience for him. He is a man of great detail, a serial winner, he will be questioning himself, searching for the answers. We talk about stress in management. I kicked bottles over, punched walls, I smashed a television in the dressing room at Dunfermline. I acted like a child, lost control of all emotion and what did the players learn from it? Nothing.
"This is not about what Pep does, it is about his players and what they do to regain belief.
"When I was playing at Liverpool in 1981, we lost 3-1 to Manchester City at Anfield on Boxing Day. It left us in 12th position in the league, nine points behind the leaders. The headlines were all about 'End of the Empire', 'the Empire is crumbling'.
"That hurt because at Liverpool you were constantly reminded of the great players who had gone before and the dynasty they had created.
"A couple of days prior to our next game, an FA Cup tie at Swansea, Joe Fagan, Bob Paisley's assistant at the time, took us outside at Melwood, Liverpool's training ground. I can remember the exact spot, there should be a bloody commemorative stone there, just on the edge of the A team pitch.
And Joe said: 'Right you buggers, that's it. We've said everything we can. Now it's over to you. I suggest you take yourselves for a night out and sort it among your bloody selves.'
"Like all footballers then, we didn't need much encouragement to go for a drink - but it gave us the opportunity to lay it all out on the table about what we thought we were doing wrong, to air our grievances, and have a proper talk with each other.
"We knew we had to find an extra yard, that extra belief, that extra aggression. It was also about being courageous and wanting to be on the ball when the game wasn't going our way and not hiding.
"We regrouped and we went on a terrific run, losing just twice in 25 games to go on and win the league title. Bob would later say it was the hardest one to win.
"For Manchester City now, it's about regaining that belief, that confidence. It should be there in spades given their recent history of winning trophies, and Pep will be looking for the leaders in the group to have the conversations we Liverpool players had and drag them through this mire. It's solely down to them."
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play