Owen is set to return from injury against Hull City on Saturday in a match the Magpies should win.
The 29-year-old told the Journal: “We have always been flitting around three or four places off the bottom.
“But it’s only since we lost to Manchester United and results went against us that we have found ourselves in real trouble.
“There is a determination to put it right. I don’t feel we are in the last-chance saloon yet, but it is getting damn important we start picking up points and fast.
“We have to realise we are responsible for getting results above anything else.
“That responsibility filters through to the players – from the fans, the staff at the club. Everyone’s backs are against the wall now, and nobody wants to see Newcastle United not playing in the Premier League next season.”
He added: “I definitely think it has been a fractious season, even by Newcastle’s standards.
“Regardless of that, it’s just an easy excuse for players to make if they say this has happened off the pitch, and that has happened, so that is why results haven’t been good.
“I don’t care what has happened to the chairman, the tea lady or whoever; when you are out on the pitch, you are focused on trying to win, and that’s it.
“Anyone who uses what has happened to the club this season at boardroom level, it’s just an excuse in my eyes.
“Thankfully, nobody here has been using that as an excuse.”