Palace are sixth in the Premier League following Monday's 1-1 draw at Everton, with Pardew's men on course to improve on the finishes of 10th and 11th in the last two seasons.
Arsenal counterpart Arsene Wenger suggested on Friday that as many as eight teams could challenge for top honours in an unpredictable campaign that sees Leicester City as surprise leaders.
And Pardew told reporters: "Wenger's right, there are eight teams who could make the Champions League. We're probably on the fringes, the ninth team.
"It's a very tough league. It's been a fantastic 2015 for us and we need to match this year next year. If we do, we could end up in the top six.
"We're a long way from there. We'll start talking about that in March if we're close."
Ahead of Pardew's first full season at Selhurst Park, the arrival of France international Yohan Cabaye from Paris Saint-Germain for a club-record fee raised eyebrows.
Having integrated Cabaye into an attacking squad that includes lower-league finds such as Yannick Bolasie, Dwight Gayle and Jason Puncheon, Pardew added: "We're not going to forget our roots.
"Our roots are not signing players from PSG, some of our best players have come from non-League.
"Ian Wright, non-League player. Andy Gray, non-League player. Alan Pardew, non-League player. He wasn't as good as the first two!"
Pardew will be without Mile Jedinak (ankle) and Bakary Sako (hamstring) for Saturday's visit of Southampton.
"Alex McCarthy is returning [to fitness]. He'll be on the bench tomorrow, Julian Speroni will be next week," he added.
"Mile rolled his ankle in training and will miss this game. Gayle has had a set back with his injury, but [Marouane] Chamakh is getting sharper."