I agree with that bit, but you still got lucky imho. If Aguero scored that penalty that tie was over, then Son scores and you didn't believe your luck when you found yourself beating us 1-0. It helped that Pep didn't play Sane and KDB till the 88 minute.
Then at the Etihad somehow Laporte decided to give Son the ball so he could score and a few more mistakes on that day. Then Var referee somehow missed Llorente's handball and a few more incidents went your way. Thats a major amount of luck going your way.
Just as you said it, cup competitions allow for lesser teams to win. by talent, believe, referees decisions, Var and a huge amount of luck
We shall have to agree to disagree as to what constitutes luck and what constitutes handball!