Owing to suspension to Matt Ritchie, the Ghanaian was handed a rare start in the midweek fixture away at Goodison Park.
It was just his second first XI berth in the topflight this season, having been reduced to a bench warmer.
“I’m very disappointed that I was not on the scoresheet because I had the chances to score," Atsu told his club's official website.
"I was prepared for this game and I wanted to score and stay with the team. I’m disappointed I couldn’t score but I’m always prepared for every game and really focused.
"I want to give everything for this team and I just need to continue working hard and the next game, we’ll see.”
Salomon Rondon gave Newcastle a surprise 19th minute lead but Richarlison equalised for Everton in the 38th minute to force a 1-1 draw.
“We came here to win the game and not to draw the game,” Atsu, who lasted for the entire duration of the game, 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."
Atsu will be hoping to be handed another starting berth when Newcastle host Wolverhampton Wanderers on Sunday.
In all, he has nine Premier League outings for the Magpies this season.