"It is part and parcel of being a manager or a footballer - there is always someone ready to have a pop at you," said the England international. "I don't pay any attention to what those people think of me, and I am sure Avram doesn't either. He has got broad shoulders."
Cole, 26, continued: "There are people who will say if you win one game you are a God, and if you lose one game then you are the biggest duffer to have ever played football.
"If you look back at it, with all that has happened here, you have to say the club is going in the right direction.
"But we are not too interested in plaudits - you want trophies.
"We fought United all the way for the title and we are disappointed not to have won, but credit has to go to the whole squad and everyone around the place who have kept it going, shown real steel and determination.
"If we were to win in Moscow, then we would be going full speed ahead again.
"The Champions League final is the top of the mountain, the benchmark for any club. To win it is a massive achievement."