Laurent Koscielny and Mesut Ozil both found the net from close range in the first half before Olivier Giroud headed home a third after the break to complete a comfortable victory for the Gunners.
The defeat at the Emirates Stadium continues a miserable period for Newcastle, that has seen the club lose 12 of their 17 league matches in 2014.
Newcastle's travelling support were openly critical of Pardew and the club's owners throughout the game with one chant suggesting they would celebrate if the Magpies boss was sacked.
"They're frustrated," Pardew said after the match.
"We had 2,000 fans here tonight, they made the long, long trip and although we were playing a good team they expect us to win.
"They've seen us lose again and they're not happy and I respect that.
"All I can do as a manager is make sure I do this job to the best of my ability - we've been top 10 all year and this recent run is not something I'm hiding from."
Newcastle are currently ninth in the Barclays Premier League table, two points ahead of Stoke.
The Magpies host struggling Cardiff on Saturday and Pardew urged the club's supporters to help the players maintain their place in the division's top 10.
"We've got the best fans in the world," Pardew said.
"We should have performed better in this run and we have to finish in the top 10.
"If Cardiff fans think the game's important for them, it's important for our fans we win.
"I thought we could have got really harmed tonight at 2-0 but I think on a football basis we've come out with our dignity still intact.
"It's very, very important our stadium gives us the same opportunity on Saturday they did at Swansea when it was a good atmosphere for us to play under.
"I really hope on Saturday we give them something they deserve because they don't deserve the recent run we've offered up to them."
Newcastle enjoyed an excellent start to the season and were only four points off fourth at the turn of the year.
Pardew insists his players have to learn from their collapse and ensure the same does not happen again next season.
"In the first half of the campaign people might say we excelled to a degree but I thought we gave good value for money for this football club," Pardew said.
"But in the second half we haven't and next season we have to make sure we give the fans full value for the investment we have made through the 38 games."
Arsenal's victory means the Gunners need just one more win from their remaining two matches to guarantee Champions League qualification for a 17th consecutive year.
Manager Arsene Wenger admits the Gunners want more than a place in the top four but insists injuries to key players took their toll on the team's title challenge this season.
"We had Theo Walcott, Jack Wilshere, Mesut Ozil, Aaron Ramsey and Koscielny all out in the same period - you can miss one or two but four or five will affect any team," Wenger said.
"Finishing in the top four shows the club has been consistent over the years
We want more but at the crucial period of this season we lost many players.
"We have shown we have potential but we want more next season."
Source : PA
Source: PA