Newcastle came close to claiming a point on a couple of occasions, but Allardyce was happy with the overall display from his players at St James' Park to move level on points with Watford in ninth place.
"I'm pleased for the main, but there's obviously room for improvement," Sky Sports News quotes him as saying. "We played on Sunday, they played on Saturday, so we didn't have as much recovery time. But with a couple of adjustments here and there, we're rolling on.
"It's another goal for Wayne. After a bit of an iffy start, we played our way into the game and played well, using the ball a lot better. I'd have to say the goal was a terrific move. There was a one-two with a flick around the corner and then played down the side.
"I felt Newcastle's chances were a couple of great strikes from long distance so we limited them to few chances and that gives you a platform to go up the other end and get three points.
"It was an exceptionally good performance on the basis that we're perhaps running on empty after playing on Sunday with the effort we put in. The defence have done a fantastic job and that has been the bedrock to our upturn in fortunes. We're heading in the right direction, in the top half of the table where we want to finish in May if we can."
Everton have now collected 10 points from their last four league games - one more than they managed in their previous 12.