The result saw the club close the gap on Manchester United to four points, though Erik ten Hag’s side have two games in hand.
Third-placed Newcastle United have won eight of their last nine Premier League fixtures, and Eddie Howe’s team, six points ahead of Liverpool, also have a game in hand on Klopp’s side.
Klopp was asked after the Fulham game if Champions League qualifcation was still possible for the club.
“I have no clue,” Klopp told Sky Sports. “You have to ask Newcastle and Manchester United what they think about it.
“Our only chance is to win football games, and we will see. The final table is always a reflection of the performances you put together over the year.
“Even that (fifth place) is not sure yet, as we have super strong competitors – Brighton, Tottenham obviously, Aston Villa around, Brentford probably, Fulham as well.”
Howe was asked about Newcastle being potentially two wins away from Champions League qualifcation after last weekend’s 3-1 home win over Southampton.
“I think from my perspective, and on behalf of all the players, we want to try to win every game,” said United’s head coach.
“We’ve got a very tough one to come next here (against Arsenal on Sunday), which will be a great occasion for us, and that’s the only focus that I’ll have on it.”
Newcastle, relegation contenders last season, have taken 65 points from 33 games so far this season.