Having lost their opening two Premier League matches, the Magpies have now won their past three to climb into the top four of the table.
Benitez, however, wants his side to stay grounded as they navigate a tough league and look to avoid an immediate return to the Championship.
"We have won three games but at the same time, I know that it is quite difficult and we have to keep feet on the floor because it will be a long race," the Spaniard told Sky Sports News.
"When I came at the end of the 2015-16 season, we had around 33 players and now we have 26. Of that 33, a lot of them knew they would not be here in the future so the atmosphere was different. This 26 know that they are here and they will stay for some time.
"The fans, when they talk about this club, they say the players care about the black and white shirt. I think that is the main thing. The other group were professional but some of them were finishing their contracts and there were too many.
"With any club, if you have the team doing well, the fans talk about football. I would like to have the same situation until the end of the season because that means it will be positive. I'm really pleased with that because to see a city and the fans dreaming, of course we sometimes have to keep our feet on the floor, especially at the start, but I'm not worried about the fans dreaming."
Up next for Newcastle is Sunday's Premier League trip to fellow new boys Brighton & Hove Albion.