Bottom side Jambos found themselves trailing to a Steven Thompson goal after just two minutes of Sunday's Scottish Premiership clash in Paisley, before Jamie Hamill struck to secure a share of the spoils.
Next up is the visit to Easter Road on Wednesday for the third Edinburgh derby of the season, with Hearts having come out on top on both occasions so far despite their well-documented problems.
Paterson - who netted the winner against Hibs at Tynecastle in August - said: "We have won there already this season and we have beaten them twice this season so we need to try to make it three out of three."
Hearts - who were docked 15 points for going into administration - now sit on minus two points following the draw in Paisley, which saw them end a losing streak of five games.
Paterson added: "Three points would have taken us to zero and the only way is up from there.
"We need to start taking advantage of teams like Ross County and Partick Thistle slipping up and we need to start gaining points back.
"We are off the losing streak now. We are just one win away from that zero so we just have to see what we can do in the next game.
"If we hadn't lost a sloppy goal in the first couple of minutes of the game, we would have taken all three points.
"We just have to eradicate those mistakes from our game. It's silly mistakes that are costing us games."
Paterson could have secured maximum points for Hearts deep into injury time but was denied by a superb save from former Jambo Marian Kello.
He said: "I couldn't have caught it any better and it was just a great save from the goalkeeper."