Florian Wirtz put Liverpool ahead in the first half, but Marcus Edwards equalised against the run of play after the break, extending a worrying pattern at home. Slot's side have now failed to beat any of the Premier League's newly promoted teams at Anfield this season - a sequence not seen since 1980-81.
"There wasn't booing in my head, it was frustration," Slot said. "If we as Liverpool are not disappointed with a draw at home to Burnley, then something is completely wrong. I understand it completely - I feel it, the players feel it, and the fans feel it."
Liverpool dominated the match, posting 32 shots, 11 on target and an expected goals figure of 2.95, while Burnley scored from their only effort on target. Cody Gakpo had a chance cleared off the line, Wirtz went close again and Dominik Szoboszlai missed a first-half penalty that could have altered the outcome.
Burnley's equaliser came after Liverpool failed to play out cleanly from the back, something Slot admitted has been a recurring issue. "That moment sums up a large part of our season," he said.
Although Liverpool are now 12 games unbeaten, Slot played down the significance of that run, stressing higher standards are required. The Reds sit fourth in the table, just one point above Manchester United, having dropped points in several games they dominated.
"We can talk about being unbeaten, but our standards are winning games," Slot said. "We've dropped too many points when we didn't deserve to - and that's on us."
The Reds are expected to be boosted by the imminent return of Mohamed Salah, with challenging fixtures ahead against Marseille and Bournemouth.
Mikel Arteta was left frustrated after Arsenal's title charge lost momentum in a goalless draw against Nottingham Forest, insisting his side were wrongly denied a decisive penalty late in the contest.
Cristian Romero admitted Tottenham are going through a "disaster moment" after their damaging 2-1 home defeat to West Ham, a result that has increased pressure on head coach Thomas Frank.
Chelsea, Liverpool and Tottenham Hotspur were all in action on a gripping Premier League afternoon that delivered late drama, missed chances and major talking points.
Crystal Palace are preparing for life after Oliver Glasner, with the Austrian confirming he will step down as manager when his contract expires at the end of the season, bringing an end to a transformative but turbulent era at Selhurst Park.
