Cole was delighted for United after their Champions League win in Turin.
And the former City striker said, “Today is a massive result because I'm not sure how many people expected Man Utd to go there and get a win.
“For me, I thought if they left with a draw, it would have been a real positive result because Juventus have been so strong at home but to come away with a win, it's a big result, especially with the derby at the weekend.
“Everyone will be buzzing with that result. It's a major, major boost and Jose Mourinho will be delighted as will everyone flying home tonight.
“You look at the two other games now and Man Utd really have to be looking to qualify - well not looking to qualify, they should qualify.
“But as we know in football, anything is possible. There will be another tough game in Spain against Valencia and the next two games will sort the group out for Man Utd."