The hosts staged a late rally when Erik Lamela thrashed home in stoppage time. Despite the scare, Liverpool held on for the three points.
"I'm not a personality to wait for problems,” said Klopp. “But I'm old enough to know they will come.
"Nobody will play the perfect season. It's still early - five games but it is fantastic that we have won all five and improved. I like that development. Now we have to prove that and do it again and again."
Liverpool finished fourth behind Manchester City, Manchester United and Tottenham in the 2017/18 season.
But after beating Pep Guardiola’s Manchester City in the last season's Premier League and Champions League, Klopp’s men have been anointed the squad most likely to challenge City for the 2019 title.
"I'm really happy and proud about the performance at Tottenham,” added Klopp. “Because the boys came back from international duty only on Wednesday and Thursday.
"With all good results, of course you have momentum. Now we won a few games, that's good, but it doesn't change anything for us. It's a long season.
"I'm happy with my squad, it's really good, but we will have problems in the season. How we deal with that, I don't know."
Only Chelsea and Watford have won their opening four games in the Premier League.
Chelsea host newly promoted Cardiff City at Stamford Bridge and Watford entertain Manchester United on Saturday.