Twice the Reds appeared in a commanding position as they led 2-0 through Hugo Ekitike’s double and even bounced back after Leeds levelled at 2-2 to restore their advantage thanks to Dominik Szoboszlai’s strike.
However, the vulnerability of Slot’s men from set pieces cost them once more when Ao Tanaka fired in from a corner deep into stoppage time,
Liverpool have now won just two of their last 10 Premier League games and four of 15 in all competitions to put Slot under pressure despite his title-winning debut season at Anfield.
"It is not the first time we drop points, not the first time we concede a goal in the last minute, or we concede a goal from a set piece," said Slot.
"The only ones to blame are ourselves. If you score three goals, it should be enough to win a game, especially when we don’t concede many chances."
Slot left Mohamed Salah on the bench for the third consecutive game and did not even introduce the Egyptian as a substitute.
Club record signing Alexander Isak was also left out, but Slot’s decision to start Ekitike over the Swede was justified by the French international.
Salah is set to depart for the Africa Cup of Nations after Liverpool’s next two matches, and Slot refused to be drawn on what the future holds for the club’s third-highest goalscorer of all time.
"Today it felt to me we needed different players to bring the win over the line," added the Dutchman on not bringing Salah on.
"We have to accept the situation we are in. The short-term future of Mo is he goes to the AFCON, but first we play Inter and Brighton."