Newcastle are second from bottom after winning only six games this season and the pressure on the former England coach is mounting.
"I'm very disappointed. That was definitely a poor performance and 'going down' material," McClaren told the BBC.
"We have got to find the fighters in the team and the performance today did not epitomise that. We cannot play like that and hope to stay up."
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Newcastle fell behind to Steven Taylor's first-half own goal and the St James' Park crowd, who have not celebrated a major trophy since 1969, turned on McClaren at halftime.
"We are fortunate we've got 10 games left and that's enough," McClaren said. "It's a four-team league now and we play everyone around us."
Newcastle have 24 points, eight ahead of bottom club Aston Villa, level with Norwich City and one behind north-east rivals Sunderland.
"There was a certain edginess and you could see that in our play," McClaren said.
"We lost our shape. Normally we are a good attacking team but today we were poor on the ball. You can only say that the pressure got to them."
McClaren, assistant manager to Alex Ferguson at Manchester United before taking charge of Middlesbrough and the England team from 2006-07, remained defiant.
"I can't see any positives but we have to stick together as a staff and as a team and fight," he said.
(Reporting by Ed Osmond; Editing by Tony Jimenez)
