Brendan Rodgers’ side were hammered 7-0 in their Group C opener against Barcelona earlier in the month and come up against a high-flying Sky Blues side who have won their first 10 games of the season under new boss Pep Guardiola.
Northern Irishman Rodgers claimed his side were too passive in the Nou Camp and Brown knows it has to be different against the Premier League leaders.
The 31-year-old midfielder said: “It’s about getting touch tight. We sat off Barcelona and admired them more than anything, letting them play and show what good players can do to you if you sit off them.
“We need to get touch tight, get our bodies in and try to win the battles all over the park.
“We’re going to have to work as a team. We’re going to have defend a lot better than the last Champions League game, we’re going to have to composed on the ball and take our chances if we get them.
“Watching them this season, City have changed their style of play.
“Guardiola has come in and brought a different style for them which seems to be working in the Premier League so far.
“We’ve got a gaffer who’s tried a different style for us and it’s been working in the Premiership.
“It will be a good proper game of football, both teams like to get the ball down and play it.
“It’s always going to be hard playing against good players, but we need to show our qualities and step the game up a little bit.”
If City are victorious against the Ladbrokes Premiership leaders, they will equal Tottenham’s 11 wins on the bounce from the start of the 1960/61 season.
However, defender Aleksandar Kolarov prefers to look at the biggest picture.
He said: “The records are always nice but in the end if you don’t win the title, who is going to remember?
“I don’t know who was the last team who had 11 straight wins but the people remember who won [trophies].
“The records are always there to beat and somebody is one day going to come and get 20 victories in a row.
“It’s always good when you are winning but the titles count not the records.”