Yes and No.
Yes because he ended up giving his near post away when he really should he spread his body a bit better.... but no because the space rose had, if he doesn't come out rose has time to touch and give himself a better angle to shoot on goal, mig had to close the space down but in doing so he didn't cover himself well.
If we had Hart in goal we win.
Ming is shite as we all agree on here, but don't think you can say having Hart in goal automatically means we'd have won. You have to question the defending that firstly allowed Dier to cross, missing the header and then clyne getting sucked in before even getting to Ming. By your method we could say, had coutinho wore the correct boots we should have won.