The Eagles face fellow top-flight side Southampton in what Pardew has described as a "difficult" game but he is confident the team have the chance to succeed.
He said: "I think teams not being as powerful or as fluid as they were (leaves the FA Cup open)
I can talk about last year with Chelsea and Manchester City better placed than they are this year
"There is a better chance I think to win it this season for the likes of ourselves, Everton, Stoke and one or two other teams.
"Like at Newcastle, I think they could win this competition and if we didn't win it, I hope they do."
Pardew believes the FA Cup is still of great importance to all the clubs and that teams focus on the cup games as much as they concentrate on the league.
"The teams in the lower end of the Premier League, of course (relegation) does impact upon you financially and I don't think anyone who loves the FA Cup could not understand that, that makes sense," he said
"But I don't think the big clubs underestimate the importance of it now and I think you're going to see that with selection at the weekend."
Crystal Palace currently sit seventh in the Premier League but Pardew believes that he would show the same level of enthusiasm for the FA Cup no matter where they were in the table
The 54-year-old says he has always enjoyed the competition, having reached the final as a player (with Palace in 1990) and as a manager (with West Ham in 2006) and he believes it is something that managers have to balance
He said: "I can't win in this press conference - I'm either not concentrating on the FA Cup or not concentrating on the league.
"I'm concentrating on both
I've cast an eye on Tuesday (when Palace play at Aston Villa in the league) as all the Premier League managers will do
"We've got very important Premier League games
Ours is against a team that is currently bottom of the table so we have a chance in that game to get another away win
"But that isn't going to take my focus away from the FA Cup.
"It's very much the message I'll give the players that this is top of our agenda this week, above Villa and above Man City."
Bakary Sako is available for selection against Southampton after being out with a hamstring injury since November
Midfielder Yohan Cabaye is also back after serving a one-match suspension but Yannick Bolasie (hip/thigh) and Kwesi Appiah (knee) are still absent
Connor Wickham (calf strain) and Dwight Gayle (hamstring) should be fit again for the game against Villa on Tuesday.
Source : PA