West Ham, meanwhile, were on the wrong end of a hammering as they were beaten 4-0 by the reigning champions Manchester City.
Newcastle did not win a game until their 11th game of the season.
"Felipe [Anderson] played a very good game also today".
"We need to analyse the goals, have a look again at the mistakes we made, see where we need to improve".
Perez headed over from close range after meeting Ritchie's 27th-minute corner and then dragged a shot wide, but his side was living dangerously and Arnautovic might have increased the Hammers' lead in the meantime had either Aaron Cresswell or Anderson been able to produce a better final ball. The lack of offense would be more concerning for Newcastle if the club was not so good defensively.
Benitez's side had chances to equalise at a soggy St James's Park, but a second goal from Hernandez ended hopes of a comeback.
They got their noses in front courtesy of Javier Hernandez's 12th-minute strike and then picked off the Magpies at will with a display of lethal counter-attacking football.
Pellegrini said: "If you review his career, Javier had played at Manchester United, at Real Madrid, at Bayer Leverkusen, in the national squad of Mexico, different countries and everywhere he has scored".
Andy Carroll took has done full training during the course of the week and like Wilshere, he too is expected to start the Newcastle vs West Ham game on the bench. We'd had three victories in a row, and wanted to show our fans we could give them another one, but sometimes things just don't go the right way for you.
He was unsafe on the break, finished with the highest passing accuracy of any West Ham player who started the game and was deserving of his late goal. So, I think that Javier, he is very important for our team.
Anderson's pace down the left caused Newcastle all kinds of problems, but it was Mexico worldwide Hernandez who put them to the sword.