Goals from Fabian Schar and Sean Longstaff sealed the victory at St James' Park, which moved the Magpies seven points clear of the relegation zone.
Benitez, though, does not think their battle to stay up is over yet.
"Obviously, winning games gives you more confidence, but we have to have the same idea of one game at a time," said the Spaniard "We are where we are because we are focusing on each game.
"The job is not done, no chance. We need to approach every game with the same mentality. The players know that, and the fans do, too.
"The players deserve the credit; they were doing really well. They fought for each other in the second half. It was a good win against a good team.
Part I of Matchweek 28 pic.twitter.com/MYtHwXem3g— Premier League (@premierleague) February 26, 2019
"I was not thinking too much about how many points we could be clear, just to carry on doing what we know we can do well. We went to Spain and trained really well, and we came back and are in the same situation. The players work hard and are keen to do the right things. They want to be solid as a team and be a threat."
"He is someone that was training with us and doing well," he said. "We knew he would have a chance, he was lucky with our injuries to play sooner than we expected, and he did well, so we kept him in the team.
"He is working hard and listening to staff and learning, which is the main thing. Having a young lad from the academy is a great example for people to follow. It is ideal for any club to have players through the academy because they are cheaper, and they give you more."
Burnley boss Sean Dyche felt his side were well short of the standards that had seen them go eight league games without defeat, a run which included the 2-1 win over Tottenham on Saturday.
"It was a really poor first half, a long way short of where we have been," he said to BBC Sport. "I don't want to be too critical. We just didn't have the fight we have had recently. Credit to Newcastle - they played well. Even not playing well, we had two big chances.
"We were at the races in the second half, we huffed and puffed a bit, created some chances and a couple of scrambles."