The club’s fans again chanted Benitez’s side during Saturday’s 1-1 draw against Watford.
And there will be another show of appreciation at St James’s Park tomorrow night when the club takes on Manchester United.
Newcastle, 15th in the Premier League table, go into the game needing a result, with the gap between themselves and the relegation zone having been cut to just four points at the weekend.
“I think our fans are quite clever,” said manager Benitez.
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“I decided to stay when I came here, and I thought we could save the team, but we couldn’t. I decided to stay in the Championship, so they know about my past, about my history.
“They appreciate that, and then we won, which is football. If you have a good CV, you still have to win. And we did it – we won the Championship.
“Not too many managers go from Italy, Spain and win everywhere they go, like to the Championship – or even stay in the Championship and then win.
“I think that the fans appreciate that. I think they also appreciate that we work with a methodology, with ideas of how to improve the clubs, how to be stronger, and about the ambition that we have.
“So I think that they appreciate that, and that is the reason why they support the team and the manager.”
Asked if it was a nice feeling to have that support, Benitez added: “Obviously, to have the fans behind you is also a very good feeling.
“But, at the same time, you want to have the fans behind you winning games, so they will be happier, and everybody will be happier. We’re trying to do our best.”