The Magpies marched towards the top four with seven wins in nine games, but they slipped back to seventh after Olivier Giroud's goal sealed a 1-0 win for Arsenal at St James' Park.
Debuchy believes Newcastle can still hold their own with the big guns and urged his team-mates to produce a response in the New Year's Day trip to West Brom.
"We are not really fixing any limits as to where we think we can get, and we are going to aim as high up the league as we possibly can and get as many points as we possibly can," he said.
"Sunday was a setback for us, but we have to try to get back on track, go away on January 1 to West Brom, get as many points as we can, take one game after another and see how far we can go."
Debuchy joined the Magpies from Lille in January and admits the French fixture schedule is much less intense over the festive period.
But the full-back has welcomed the physical challenge of playing a string of games in a short period of time.
"It's the first time I have experienced the Christmas and New Year football period here - in France, we have a week, maybe 10 days, off," he said.
"But it's quite nice to get those games coming thick and fast and I feel more than ready to get out there and attack these next games."