The Reds enjoyed a superb campaign in 2018-19, winning the Champions League and finishing second to Manchester City by a point in the Premier League with a club-record tally:
Liverpool are still without a league title victory since 1990, though, while they have won the Champions League twice during that period.
But Klopp, speaking ahead of Liverpool's UEFA Super Cup clash with Chelsea in Istanbul, Turkey, on Wednesday, said his side cannot choose whether to go after one specific trophy and must only focus on winning every match, per Sky Sports:
"Unfortunately I am not good enough to decide that! I have to take what I can get. That is how it is. We didn't decide last year that we would go for the Champions League and ignore the Premier League obviously so we just try to win the next football game. That is [Wednesday] night and that is difficult enough. I am not a genius so I have to take what I can get. Last year thankfully we won something, celebrated it, so now let's carry on."
Liverpool opened the new Premier League campaign in fine fashion on Friday by beating Norwich City 4-1 at Anfield.
Defending champions City, though, then responded with a 5-0 away win at West Ham United on Saturday.
The Sky Blues and Klopp's Liverpool were a class apart from the rest of the English top flight last season, with the Anfield giants finishing 25 points clear of third-placed Chelsea.
It is widely expected that the two clubs will again be the only two realistic challengers for the title in 2019-20:
Liverpool have been dealt an early blow in the campaign after Alisson Becker picked up an injury against Norwich that will leave him sidelined for the next few weeks:
One of the key improvements Liverpool made last season to propel themselves from also-rans into title challengers was a huge improvement in defence.
They conceded just 22 goals in the league in 2018-19, the best record in the league, after averaging over 43 goals conceded in the previous nine campaigns.
The addition of Alisson from Roma last summer, as well as the signing of Virgil van Dijk in January 2018, were key to that improvement.
Summer signing Adrian, an experienced 'keeper, will take the gloves during Alisson's absence, but he cannot afford to take time to settle as Liverpool have no margin for error in the Premier League title race due to City's immense quality.