The keeper replaced Neil Alexander in the second half at Ibrox as goals from Danny Wilson and Osman Sow clinched a dramatic 2-1 win.
Now the former Gers shot-stopper is confident Robbie Neilson's side can mount a powerful bid for the Championship title.
He said: "We were great on Sunday. To beat Rangers at Ibrox is a superb result at any time and, of course, it puts a marker down for the rest of the season.
"Hearing their fans booing their own team played into our hands. It told us we were doing something right.
"We passed the ball well with some good ideas. I think things are looking up for Hearts.
"We have really good players here. Technically, they are different class.
"Hearts are a massive club and we need to get the foot down now."
Gallacher started only three games for Rangers in his five seasons there, although he played on loan for Cowdenbeath, Forfar and Airdrie.
With Alexander ruled out for a month with a fractured cheekbone, the 25-year-old keeper is determined to seize his chance as Hearts gear up for their derby clash with Hibs on Sunday.
He said: "It was great to get on at Ibrox and play against a few of the boys I grew up with.
"Hopefully I can now stake a claim to keeping the No.1 jersey here. As a professional, you need to prepare right and hope to get your chance. That is all you can ask for."