Well Liverpool came 2nd and City came 3rd so it's not like they play dirty. It's just the fact that whoever is top of the league gets a place in Europa league.
The Fair Play league is competed by teams in the Premier League.
The idea is if you commit the least fouls, red cards and yellow cards (all measured via a points system) then you get a place in Europe.
Obviously if you qualify for Europe on via league position/FA Cup appearance/ League Cup...