The Toon have endured a difficult last week, crashing out of the Europa League at the quarter-final stage to the Portuguese giants before being outplayed by their bitter rivals at St. James Park on Sunday, losing 3-0.
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"I can understand that it’s very difficult for the supporters, but it’s also very difficult for us to take a defeat like that," he told reporters.
"But I just want to tell them that we really need their support, it’s important for us so I hope they’ll stay with us - they’re a really important part of the club and for us.
"I want to let them know we’re going to fight until the end.
"Quite simply, the manager was disappointed - with the result and the manner of the defeat. He said we need to get out there and work harder and make sure we get the results we need."
With just five games left in the season Newcastle still need points to secure their top-flight status for another season, with the next opportunity coming on Saturday away at West Brom.
"We don’t have a choice but to get on with it," Debuchy added.
"We’ve got some important matches coming up and that starts next weekend. We need to get to work and make sure we’re up for it and we’ll start next week."