The Magpies were humiliated in Sunday's Tyne-Wear derby as they suffered a 3-0 loss to their local rivals, marking Paolo Di Canio's first win as manager.
That result followed Newcastle's exit from the UEFA Europa League in midweek when they lost to Benfica in the quarter-finals.
France international Debuchy insists the players took Sunday's defeat as hard as the fans but says the Magpies are determined to keep fighting as they look to secure their Premier League status for another year, starting at West Brom on Saturday.
He said: "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.
"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.
"We don't have a choice but to get on with it. 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."