I think you owe the coaches a new goalie before firing them. They outshot the Sharks 41 to 18 and got 61% of the expected goals at 5 on 5. They outshot Vancouver 46-24 the previous game with 56% of the expected goals at 5 on 5. I have a really, really difficult time putting those two games on the coaching staff. I only watched about half of each game, but my eyes saw a team that can't buy a goal and can't get a save.
I won't be surprised if the coach is the one who takes the bullet here, but I think their problem is much more goaltending than coaching at the moment.
Edit: I just looked at gamelogs and good lord the goaltending is somehow worse than I was thinking.
Campbell's SV% in losses: .750, .875, .806, and .853
Skinner's SV% in losses: .750, .750, .889 (OT loss), .906, .852, .833, and .833
Honestly, what can the coach do with that? Edmonton is 2-1-1 in games where the goalies put up an .880 or better.