Huddersfield snatched a late goal against Leeds to run out 2-1 winners against their local rivals at the John Smith's Stadium.
David Wagner sprinted down the touchline to join in the celebrations following Michael Hefele's 89th-minute goal.
This sparked a mass brawl on the touchline, resulting in Monk and Wagner both beng sent to the stands after squaring up to eachother.
And the Leeds boss has accused the former Borussia Dortmund man of showing a lack of class and humility following the goal.
"I can only speak for myself, in my world where I've been brought up my values are to have humility and to have respect and a bit of class," Monk told Sky Sports.
"When I don't see that [from David Wagner] I feel upon myself to make sure that is put right.
"It is what it is, I don't make anything of it but i live my my values and these values I hold dearly to myself and to my team – they live by that.
"When we see that against us then it's obviously not a good thing to see."