Looking to bounce back from their 4-3 home loss to Barca at the weekend - Real's first defeat in any competition since October - Carlo Ancelotti's men took the lead at Sevilla on Wednesday night through Cristiano Ronaldo's deflected 14th-minute free-kick.
However, Sevilla were level within five minutes through a Carlos Bacca strike, and the Colombia international then stunned their star-studded visitors by netting what would prove to be the winning goal 18 minutes from time.
The 2-1 defeat left Real three points adrift of Atletico Madrid at the top of the table and two behind Barcelona, with both their title rivals winning on Wednesday.
To make matters worse for Real, they are essentially another point further back on Atletico and Barca because they have the inferior head-to-head record against both teams this season.
Real now have eight games left to try and claw back the top two and Marcelo assured fans the players will do all they can to achieve that.
The Brazil international said on his club's website: "We created chances but we were unable to make the most of them, that's football. But we would like to apologise to the Real Madrid fans, who always support us.
"We knew the end of the season is very difficult, with very important matches and we will keep on fighting."
Marcelo's fellow defender Pepe added: "I congratulate Sevilla, we tried to win but couldn't do it.
"There are still games left and we still have a chance.
"This defeat has nothing to do with the Clasico (against Barca), these things happen in football.
"Now we have to be ready to win on Saturday against Rayo (Vallecano)."