Goals from Papiss Cisse (2) and Hatem Ben Arfa enabled the Magpies to move level on points with fifth-placed Chelsea in the Premier League before Shane Long's second half consolation effort.
But Pardew believes Newcastle are not well enough equipped to overhaul one of the top four.
Pardew said: "Are we Champions League contenders? I don't think so. The last 10 games are the most important ones in any season and we've won the first two of those.
"There are a lot of games left, a lot of points. But I don't think we've got the depth of squad to challenge for that (a Champions League place).
"I get told the fans might be thinking `this is on' - but not me."