"Of course we are more focused on ourselves," Mane told Sky Sports.
"But sometimes we look when Manchester [City] is playing, we have more pressure than if we play ourselves!
"I want them to lose, and they are so good, and sometimes it's difficult for them to lose."
Mane and Liverpool host Tottenham at Anfield in their next game in arguably their toughest fixture of the remainder of the season, but the pacy forward warned that any one of their final fixtures could cause them to slip up.
"It could be [the toughest game], but people expect the only tough games to be against the top six, but sometimes that's not the case because it's unpredictable.
"It could be Southampton. Sometimes you win easily with the top six, and sometimes you get a difficult game, but it's the same with the teams at the bottom of the table.
"So it would be a bit silly to say Tottenham would be the biggest game."
Mane also urged calm around Mohamed Salah's goal-drought, with the Egyptian failing to find the back of the net in seven games.
"People out and around the club are speaking about Mo because he used to score almost every single game.
"It's almost normal because it's football, but we all know him as somebody who is very, very relaxed with the situation. Sometimes it can happen.
"But I would especially love to see him smiling by scoring goals. We try to help him score more goals for him."