City stormed into a 3-0 lead in the first six minutes and by half-time had made it five without reply to set a new Premier League record for an interval lead by a team away from home.
Emmanuel Adebayor was on the mark twice and Craig Bellamy, Carlos Tevez and Patrick Vieira scored one each in the opening 45 minute romp which set up the win in atrocious conditions.
Vincent Kompany made it six after the break before Steven Fletcher pulled back the merest of consolations for beleagured Burnley with 19 minutes to go.
"It is a good position to be in and an important one. But it will be more important at the end of the season," Mancini said.
"We have some difficult games ahead and we need to show the kind of concentration we did today.
"If we do that we have a good chance as it is going to be a battle with Liverpool and Tottenham.
"I am very happy because we played a good game especially in the first 25 minutes, we were focused as we wanted to win the game.
"We pressed high up the pitch and had a lot of ball in and around the box which gave us some chances.
"The weather was not good, and in the second half it was difficult to play football.
"It is important Emmanuel and Tevez carry on scoring until the end of the season. But if you have other players who can score as well it is a bonus.
"Emmanuel's fitness is improving after a month out and he was better today than against Wigan."