Liverpool need Arsenal, Man City 'crisis' to win Premier League - Klopp
Klopp tasted defeat in front of a crowd in the Merseyside derby for the first time to leave the Reds' title hopes hanging by a thread.
Liverpool trail Arsenal by three points with four matches remaining and are just one point clear of City, who have two games in hand.
"You can read the table. We need a crisis at City and Arsenal and we need to win football games," said Klopp, who is nearing the end of his tenure at Anfield.
The German had enjoyed a dominant record over Everton with only one previous defeat in 18 games, but his final taste of the Merseyside derby was a bitter one.
"It was not the most inspired performance," added Klopp.
"I really feel for the people, I'm really sorry for that. People tell me before about record in the derby. It feels really different (to have lost).
"It was unnecessary but it happened."
A run of four wins in nine games has seen Klopp's men crash out of the Europa League and FA Cup as well as falling off the pace at the top of the Premier League.
Liverpool captain Virgil van Dijk called on the players not to let Klopp's farewell fizzle out with a whimper.
"I think everyone has to look in the mirror and look at their performance and if they’ve given everything. Do they really want to win the league?" Van Dijk said.
"We weren’t good enough. We all have to do much better. We can't let the season go out like tonight. We have to do much better in every sense."