Benitez's side now sit fourth in the Premier League table as a result, but he stressed that it is far too early to be discussing league position.
"I haven't seen the table and I don't want to see the table, believe me. I said one game at a time and now it's just to be sure that the fans enjoy it," he told reporters.
"They can enjoy it, we have to enjoy it, but we have to be sure that the next training session, we start correcting things and improving things and doing things in the way we are doing things at the moment. That's our responsibility.
"The main thing is that, the togetherness, the work-rate, the character, the whole team, the connection with the fans because the fans appreciate that. I put in the programme notes that this is something that's really important, players who want to stay, want to fight, want to defend the black and white shirt, and they are doing that.
"The fans, they appreciate that and for us to do that every week and the captain leading by example is something that you have to be really pleased with."
Newcastle take on Brighton & Hove Albion in their next league game looking to make it four top-flight wins on the bounce for the first time since November 2014.