Forest move up to 29 points, enough for 17th spot in the table on goal difference ahead of a West Ham United side that slipped back into the bottom three, despite their unlikely draw with Manchester City on Saturday.
Though Forest could have ended the day as high as 16th had Dan Ndoye's 63rd-minute strike been allowed to stand, coach Vitor Pereira was delighted with the point and their performance.
"This is not a speed-race, this is a marathon until the end - this was a chance to get the three points, but the next game is another chance," he told Sky Sports.
A half-time replacement for Nicolas Dominguez, Ndoye threatened the space between Fulham's goalkeeper and backline throughout the second half, with fellow substitute Taiwo Awoniyi also injecting some much-needed urgency into the Forest attack.
"We needed to refresh the team to put more energy in, they are players who are strong one-on-one. Dan Ndoye is fast in the space and Taiwo was fantastic. This is the spirit I want to see in my players," Pereira said.
In the 63rd minute, Ndoye latched onto a pass from Neco Williams and deftly steered it past Matz Sels, but the joy was cut short after a VAR review found him to have been slightly offside when the ball was played, and what would have been a vital goal was chalked off.
However, the decision left Pereira more philosophical than disappointed.
"Today, they tried everything to get three points - the result is difficult to control, but we can control what we do on the pitch or we can show the spirit to win the game. I am happy with them," he said.
"It will be tough until the end. The decision will be at the end, I think. I hope we can get points to escape the relegation zone. Tottenham (Hotspur), West Ham, and Leeds (United) are good teams."
