Sean Dyche's side moved within one point of safety thanks to George Boyd's goal against the champions, ending a run of seven games without a win.
Burnley may have been in the bottom three for the majority of the campaign, but Mee - a former City youth team player - hopes Saturday's win can provide the spark they needed.
"We can build on this now, take a lot confidence from it and if we carry on playing like this towards the end of the season, we will hopefully get many more points," Mee told the club's official website.
"The lads stayed calm last year when we were around the play-offs for promotion and there's no worry.
"We just work our socks off and hopefully we will get more positive results before the end of the season.
"We've taken four points off the champions and we've got to go to Southampton full of confidence now."
