Nuno Espirito Santo’s side needed a victory to keep pace with their top five rivals.
But Eberechi Eze’s second-half penalty put Palace ahead and, although Murillo equalised soon afterwards, Forest left south London outside the Champions League places.
Sixth-placed Forest’s attempt to appear in Europe’s elite club competition for the first time since 1980-81 is now out of their hands.
They sit two points behind fifth-placed Chelsea and fourth-placed Newcastle, with third-placed Manchester City three points ahead of Forest.
Forest have three games left, with winnable fixtures against Leicester and West Ham before what could be on a final-day shootout against Chelsea.
“We were in control of the game. We created and dominated a lot. Second half was different. Good reaction but Palace created problems,” Nuno said. “Palace are really dangerous if they have the shape. It’s important not to allow too much counter-attacks. We were positive but it’s not easy to play at Selhurst Park.
“We have to do our job at the City Ground. We play Leicester and it will to be tough. It’s for sure going to be like that all the way,” he added.
Nuno’s team were without injured winger Callum Hudson-Odoi, who instead joined the away fans in one corner of Selhurst Park.
FA Cup finalists Palace dominated the early stages, with some eye-catching interplay between Eze and Adam Wharton in front of England manager Thomas Tuchel.
Their first chance arrived when Tyrick Mitchell whipped in a cross which fellow full-back Daniel Munoz met on the volley, forcing a save from Matz Sels.
But Forest grew into the game and Elliot Anderson hit the side netting from a deep Nicolas Dominguez cross.
They almost made the breakthrough two minutes before half-time with a trademark counter-attack as Dominguez and Wood combined to tee up Anthony Elanga, but his finish was too close to Dean Henderson.
Wood was denied the opening goal by Maxence Lacroix’s block as his shot rolled narrowly wide early in the second half.
Palace went ahead on the hour after Mitchell was felled by a combination of Dominguez and Selz in the area.
Referee Andy Madley did not initially give the penalty but changed his mind after a look at the replay, with Eze tucking away the spot-kick.
Wharton went off with an ankle injury as Palace boss Oliver Glasner took no chances with his influential midfielder before the FA Cup final against Manchester City.
Henderson made a stunning save to keep out an Elanga free-kick.
But Forest levelled in the 64th minute when Murillo stuck out a leg to flick Neco Williams’ shot past the wrong-footed Henderson.
Forest rode their luck late on as Eze clipped the crossbar with a 20-yard curler before Eddie Nketiah had the ball in the net, only to be flagged offside. (AFP)
