The Magpies slipped out of the top six as a result of a narrow 1-0 home loss to the Gunners, who climbed back into first place at St James' Park on Sunday.
However, while they are setting no hard and fast targets, Debuchy and his team-mates will head for West Brom on New Year's Day looking to force their way back into the race for European qualification.
The France international said: "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.
"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 came as close as anyone to giving Newcastle the lead in a game of few clear-cut chances when he headed against the underside of Wojciech Szczesny's crossbar from a Yohan Cabaye corner in first-half injury time.
However, the game was eventually settled by compatriot Olivier Giroud when he glanced home Theo Walcott's 65th-minute free-kick.
The Magpies battered away at the Gunners as time ran down, but were unable to fashion a genuine opportunity to level, although they were almost handed an equaliser when Szczesny blasted a clearance straight at striker Loic Remy and saw the rebound go just wide of his goal.
Debuchy was left to lament the one defensive slip which handed Giroud his chance and cost his side a point.
He said: "We know he's a great goalscorer, so we knew exactly what to expect from him. He's a fantastic player and unfortunately he did score and it meant we didn't get any points.
"But I really do feel we walk away thinking we deserved a draw from that."
Twelve months to the day earlier, Newcastle had lost 7-3 at Arsenal amid a run of defeats which prompted owner Mike Ashley to significantly strengthen the squad with a transfer window spree which brought Debuchy, Massadio Haidara, Mapou Yanga-Mbiwa, Moussa Sissoko and Yoan Gouffran to Tyneside.
All five took time to settle, but 28-year-old Debuchy has firmly established himself as the club's first-choice right-back and has won rave reviews for his recent performances.
He said: "I am very happy here, especially here in Newcastle. For a player to come here and play in the Premier League is really a wonderful thing.
"The support, both home and away, by the Newcastle fans is absolutely magnificent. Again we have seen at home - we have lost, but they stayed back to applaud us at the end of the match.
"I think Newcastle fans have to be some of the very best in the Premier League."
The latest additions to the club's French contingent are currently coping with the demands of the busy Christmas programme with an FA Cup third-round clash with Cardiff to come after the midweek trip to the Hawthorns.
However, while it has proved a new experience for Debuchy, he insists he is enjoying the gruelling challenge.
He said: "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.
"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."