The 52-year-old takes his side to Goodison Park on Monday evening hoping they can bounce back from a wasteful 3-2 home defeat by Hull last weekend in which they took the lead twice but could not retain it.
However, he knows that could be intensely difficult against a side which is yet to lose in the league this season.
The Toffees are under new management following David Moyes' departure for Manchester United, and Marouane Fellaini's decision to join the Scot at Old Trafford robbed them of one of their most influential players.
Asked if new man Roberto Martinez had big shoes to fill, Pardew said: "Yes, but they have signed some good players and you would have to say that they have got what looks like a stronger squad than David had last year.
"Certainly the chairman there has done his bit, and they could be the surprise package of the season."
The Spaniard is busily stamping his own mark on the players he inherited from Moyes having added summer signings James McCarthy, Gareth Barry and Romelu Lukaku to the mix, and the early signs have been promising.
Everton have beaten Chelsea and West Ham and drawn with Norwich, West Brom and Cardiff, and although they slipped out of the Capital One Cup at the hands of Fulham on Tuesday, they went into the weekend sitting in sixth place in the Premier League.
Pardew has been impressed by what Martinez has done so far, and expects a slightly different approach to the one adopted by Moyes' teams over the years.
However, he is confident the Magpies will be able to cope with that having returned to winning ways with a 2-0 League Cup victory over Leeds in midweek.
He said: "Their retention of the ball will probably be greater under Roberto.
"But what we have shown is that we have got a real offensive look about us. But we have got to make sure we are tight enough to cope with that.
"We weren't against Hull, but in the last three or four games other than that game, we have been and that's important.
"If we are going to have a more offensive look, then we have got to make sure the back door is shut.
"It was on Wednesday night. We got a clean sheet again and that was a good thing."
However, Pardew knows returning from Merseyside with something to show for their efforts will take the kind of performance his team produced in their last game on the road, a 2-1 victory at Aston Villa.
He said: "They have always been a difficult side to beat, especially at Goodison. It's a tough place to go.
"We got a 2-2 last year and we really had to work hard to get that.
"They are in good form and it's a tough game to play there."
Pardew made six changes for the Leeds game as he rested some of his key men and handed chances to youngsters Paul Dummett and Sammy Ameobi.
But his big guns are likely to return at Everton with Yohan Cabaye, Hatem Ben Arfa and Loic Remy, who scored both the Magpies goals against Hull, certain to be restored to the starting line-up.
The manager said: "Yes, for sure. They are givens when they are fit, those guys."