The Magpies hit the woodwork on two occasions in the opening half – either side of Rooney’s strike – and had twice as many efforts on goal as the Toffees over the course of the night.
However, they were unable to find a way past former Sunderland goalkeeper Jordan Pickford, with Everton picking up a first Premier League away win since January 21st.
Newcastle are now just a point clear of the bottom three, but Atsu argued they could have found themselves in a far more comfortable position had they made the most of the opportunities that came their way.
“I believe we created a lot of chances, we could have scored more goals and won the game, but that’s football,” he told nufc.co.uk. “We conceded, they all went back and we’ve tried to break through them. In the second half, I think they were more defensive, but in all we were the better team and unlucky that we lost.
“From what I have seen, I think we are improving – especially in this game, and even in the Leicester game, we have improved. They didn’t create more chances than us – like I said, we were unlucky. I think defensively we were better and offensively we were good, so that is a positive thing for the team.
“We keep fighting and working hard. The next game is the most important.”
That next game takes place at Arsenal’s Emirates Stadium, where the Gunners have lost just once in the Premier League this term.
And Atsu – who made his first start for more than six weeks against the Toffees – says United must look to produce a shutout as they gear up for the second of three trips to London this month.
“We know Arsenal will be very difficult – the same as this one. Every game is very difficult for us, but we need to keep working hard and try to keep a clean sheet,” he said.
“I’m getting better and I’m trying to get back to my best. I’m trying to improve my fitness but more important is trying to work hard to improve the team.”