The Reds trailed Aston Villa until the 87th minute of Saturday's clash at Villa Park, when Andrew Robertson came up with a leveller for the Champions League holders.
Arsenal were the last team to go through an entire Premier League campaign unbeaten in 2003-04, but Klopp is not expecting Liverpool to avoid defeat from now until the end of the season.
"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," Klopp told Sky Sports News.
"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."
Liverpool have won 10 and drawn one of their 11 Premier League matches this season, with their only dropped points coming away to bitter rivals Manchester United last month.