Liverpool’s cloak of invisibility remained intact at Villa Park when they came from a goal down to beat Dean Smith’s men after Andy Robertson and Sadio Mane’s late goals cancelled out Mahmoud Trezeguet’s opener.
The Reds have now won ten and drawn one of their opening eleven league games of the season ahead of next weekend’s top-of-the-table clash with champions Manchester City at Anfield.
Liverpool’s form has led to suggestions that they could navigate the whole season without suffering a single defeat, but Klopp believes that is unlikely to happen.
Klopp told Sky Sports: "It is not possible if you play like we did until we conceded the goal.
“It was not bad, it was actually the opposite, it was good football, but it was not the winning mentality we need.
"It is probably not possible, but we don't think about it to be honest.
“We think about how we can win the next game and the next game."
Arsenal’s ‘Invincibles’, who won the club’s last Premier League title in the 2003/2004 campaign, remain the only side to go through a 38-game season unbeaten.
Liverpool hold a six-point lead at the top of the table as they come face-to-face with Manchester City next week.
A win against the champions will bring renewed hope of winning a first league title in 30 years.
