"The biggest thing is mentality. There shouldn't be any fear in saying you want to win trophies and the Champions League being one of them," she told ESPN.
"For me, being at Lyon, the biggest thing was their mentality and having that faith in knowing they were going to win games or maybe going into games where other people were like, 'this is going to be a tough fight for Lyon' and players knowing that if we did the work then the results will sort themselves."
With the first round of fixtures not until March 3-4, Greenwood said the side is focused on their upcoming fixtures but added that they are preparing for a "tough" draw against Serie A side Fiorentina.
"I think we are playing really well. Things are really starting to click into place and we've put some good performances together," she said.
"I'd be lying if I said I don't think we're in a good place to go further than we have done before. I think we need to be confident and say we want to go all the way because there's nothing wrong with saying that. It's not arrogant. It's just confidence. We should want to say those things."
Greenwood came on as a substitute for Eugenie Le Sommer in last year's final and said the feeling of winning was the best feeling of her football career. However, she wants win it again with an English side.
"It was without a doubt the best feeling I've had in football," she added. "But I think still somewhere inside me I would love to win the Champions League with a club from England, with Manchester City and this group of people."
Atletico beat City in the round of 16 last year to advance to the quarterfinals, where they lost 1-0 to Barcelona.
Chelsea return to the Champions League this year after failing to qualify for the 2019-20 tournament.
They lead the Women's Super League, with nearest rivals City trailing by five points.
Despite their domestic success, Hayes and her side are still searching for their first Champions League title and with Atletico 10 points off Barcelona at the top of the Primera Iberdrola, they will be optimistic about their chances of reaching the quarterfinals.
The matches are scheduled to take place over two legs on March 3-4 and March 10-11.