This isn´t doping though, but a foul, or serious foul play. Same can be said about your logic, if a player for example breaks a leg in international duty, and therefore will cost a lot of money for his club not having him able to play for them, will the FA of his country pay the cost´s of his injury? or his sallary during that time of recovery?
Suarez is LFC employe, but at World cup he is representing Uruguay FA, not LFC... his club should not pay for his actions in his NT with not having him for their games in PL.