Salomón Rondón thumped home the opener at Goodison Park before Richarlison drew the Toffees level before the break.
United withstood the hosts’ pressure in the second half, and also carved out a few opportunities of their own with Atsu seeing two late efforts kept out by Jordan Pickford.
And the Ghanaian international told nufc.co.uk that while he was disappointed not to have won it at the death for the Magpies, there was enough in Rafa Benítez’s side’s performance to take heart from.
“We came here to win the game and not to draw the game,” he said. “But we got a point and we are very happy we didn’t lose this game, as Everton are a very good team. We fought really hard, defended really well and attacked well, so there are lots of positives from this game. We defended and attacked as a team.
“I’m very disappointed that I was not on the scoresheet today because I had the chances to score. I was prepared for this game and I wanted to score and stay with the team.
“I would have been very happy for this ball to be on my left foot, because I’m sure I could have scored if it was.”
Both of the wideman’s late chances fell on his unfavoured right foot, with Toffees stopper Pickford equal to the shots.
Former Everton loanee Atsu praised his team’s battling display, though, as some resolute, disciplined defending saw them recover from the weekend defeat to West Ham by taking a point back to Tyneside.
“I think they had some chances and we also had some to win the game. We knew Everton were a very good team. We fought really hard to get this point so we are happy with that now. We are looking forward to the next game," he said.
“It was very good when we scored the first goal. We wanted to maintain the one-goal lead for the first half but unfortunately it didn’t happen. In the second half, we fought really hard. I think we were very good, very solid and didn’t give them many chances, but we created some chances that me, myself, I had to score.
“I’m disappointed I couldn’t score but I’m always prepared for every game and really focussed. I want to give everything for this team and I just need to continue working hard and the next game, we’ll see.”
