Klopp singled out Burnley strikers Ashley Barnes and Chris Wood when he criticised the officials for allowing the visitors to be overly physical in Liverpool's 2-0 win at Anfield.
Liverpool had not tasted a league defeat at Anfield since April 2017.
Fantasy Premier League, Gameweek 5 tips: Raheem Sterling's hot streak makes him top pick for captain; Wild Cards can wait
Get all the tips, predictions and updates you need ahead of Gameweek 5 of the Fantasy Premier League in our weekly FPL round up.
Premier League: Sergio Aguero brace powers Manchester City to win; Tottenham suffer shock defeat to Newcastle
Pep Guardiola's City team did just that thanks to Aguero as City's record goalscorer hit another milestone with a clinical double in the south-coast sunshine
Premier League: Burnley coach Sean Dyche eye first-ever points against Arsenal after winning start in competition
Dyche said that his side Burnley will be hoping to have some luck going their way against Arsenal, saying that the Video Assistant Referee (VAR) might help them
Premier League: Raheem Sterling hat-trick helps champions Manchester City hammer West Ham United; Burnley, Brighton open with convincing victories
City had a goal ruled out for the tightest of offside calls against Sterling and Sergio Aguero was afforded the chance to retake a penalty by VAR after seeing his first attempt saved.
Premier League: Ashley Barnes scores at both ends as Burnley beat Bournemouth; Jamie Vardy brace powers Leicester to win
Jamie Vardy doubled Leicester's lead three minutes after half-time, collecting Ricardo Pereira's cross and slotting home after rounding keeper Ben Hamer.
Manchester United are in optimistic mood as they travel to Burnley on Saturday, having spent the week closing in on the signing of Alexis Sanchez, and with Jose Mourinho close to agreeing a new contract.
FA Cup: Manchester City's Pep Guardiola apologises to Sean Dyche for 'yapping' gesture during Burnley clash
City boss Guardiola gestured angrily towards Dyche, making a 'yapping' gesture at his counterpart and the fourth official, as a furious row erupted between the two following Aguero's equaliser.
Premier League: Manchester United boss Jose Mourinho says £300 million transfer purse not enough to win title
Mourinho claimed that United’s illustrious history does not guarantee them — or any similar club — success when faced with City’s huge resources.
Arsene Wenger hailed Arsenal's dramatic 2-1 win over Burnley as proof they have the character to catch runaway leaders Chelsea in the Premier League title race.
Diego Costa marked his return to Chelsea duty by scoring the opening goal in a 2-0 victory over Hull on Sunday that saw the Premier League leaders go eight points clear after Arsenal went second by coming through late penalty drama.