Manchester United trail the league leaders by four points but the Northern Ireland defender believes they might have been hard to catch had the Red Devils not won Sunday's match
Evans, Patrice Evra and Tom Cleverley scored the goals in a 3-0 victory at the Sports Direct Arena to leave United trailing Roberto Di Matteo's team by four points.
The Northern Ireland international was pleased to find himself on the scoresheet but was equally as satisfied to have contributed to a second clean sheet of the season.
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"As a defender, you want clean sheets but scoring a goal put a bit of gloss on my own performance so it was nice to chip in," Evans told MUTV.
"As soon as I made a connection with it I thought it was going in, so I was delighted with that and hopefully I can add a few more.
"You could see by the way that we started that we wanted to come out and put on a good performance. I think the main thing was that we defended and attacked as a team. We were a real unit out there and we made it hard for a good Newcastle side.
"They had big powerful lads with good goal scoring records, especially up at the Sports Direct Arena. We knew we were in for a hard game but we were up for the challenge and thankfully we were able to keep a clean sheet.
"We were seven points behind Chelsea [before the game] so it was a big gap and if we had dropped points it would have been a big task. Although it is still early on in the season, you don't want to give a team that kind of advantage so early on."
Cleverley added United's third in unique style when what seemed to be an attempted cross flew into the back of the net untouched.
The midfielder later claimed that he had always intended to hit the target but Evans was less convinced.
"There is no way he meant that," he joked. "To try and shoot from there, especially to bend it, he definitely didn't mean it. I think he was looking for Robin van Persie at the back post but it went in.
"But that was a really important time for us to score a goal because they kept pumping the ball in the box and were getting one or two chances. It was important for us to get the 3-0 lead."