The Hoops put two points between themselves and the relegation zone with a 3-0 victory over Swansea at Loftus Road, courtesy of goals from captain Joey Barton, Mackie and Akos Buzsaky.
"It was a massive win, all the lads knew that," Mackie said on Sky Sports 1.
"We've been tremendous at home. We haven't been great this season against opposition around us, so we've given ourselves a massive chance with five games remaining.
"I think we've got enough to keep ourselves in the league.
"Our home form is vital. We have two homes game left which we believe we can win.
"We've turned over tough teams on our patch so we need to win our remaining games at home and give ourselves a chance."