Everton created the better chances and finally converted one of them when the ball fell to McNeil at the back post and he drilled his shot into the net from a tight angle.
The Merseyside club moved to 18th in the table with seven points from 14 matches. Had it not been for the 10-point deduction they were hit with for breaching Premier League profitability and sustainability rules, they would be in 11th place above Chelsea. Everton on Friday lodged an appeal against the points sanction, the biggest in Premier League history.
For Forest, the defeat will add to the pressure on manager Steve Cooper with his side having won only one of their last 10 matches as they lie in 15th place with 13 points from 14 matches.
“Our mentality was excellent,” Everton manager Sean Dyche told the BBC. “It’s a restart. It’s a step in the right direction, but there are plenty more steps to go.”
“I think we’re having a solid season. Seventeen points would have been a fairly healthy return. Of course it’s changed, but the mentality and the performance levels are right.”
Everton’s Portuguese forward Beto put the ball over the bar with an empty net gaping, while at the other end Anthony Elanga fired wide when well placed.
McNeil had a low shot cleared off the line by Murillo, who managed to shovel the ball onto the post and away to safety.
The home side started the second half the brighter and substitute Felipe struck the outside of the post, the closest they came to a goal in the match.
Forest thought they should have had a penalty when Abdoulaye Doucoure grabbed hold of the shirt of Ryan Yates at a corner but VAR felt there had not been a clear error from the match officials.
“Of course I’m disappointed. It’s far from the result that we wanted,” Cooper said. “The penalty that was given against us last week (against Brighton) – if that was a penalty I think the one today is (too). I hope it gets analysed. It needs to be.”
Boos rang out around the City Ground on the final whistle as Forest looked bereft of ideas in the last 15 minutes.
“I’m frustrated to say the least,” Cooper added. “I have no problem with anything that our supporters feel because it comes from wanting to support us as best they can. We have to try and put things right but there will be no deflecting.”