The Brazil shot-stopper was dispossessed by Kelechi Iheanacho and saw his team concede their first goal of the Premier League season during their 2-1 win on Saturday.
Alisson, 25, had impressed in his opening games for Liverpool, the club he joined from Roma in a reported £66.8 million ($86m) deal in July.
Klopp dismissed any suggestions the goalkeeper was arrogant, the German saying he was glad the mistake had occurred.
"He is 0.0 per cent arrogant, but he's confident and he can do it. It's like when our centre-halves play passes," he said.
"They have to play passes and defend and all that stuff. I don't look for anyone responsible, the final one was Alisson but we should have cleared the situation before.
"It wasn't a situation where you pass the ball back. We make decisions in a second and in a second you realise, 'That was the wrong one'.
"I think that was this situation. To be 100 per cent honest I am really happy it happened, because we don't have to wait for it now."
Liverpool are top of the table heading into the international break, with their next outing a trip to Tottenham on September 15.