Real enter the tie at Anfield with an hill to climb, especially after succumbing to a 1-0 defeat to the Reds at Santiago Bernabeu in the first leg.
"We are capable of beating Liverpool at Anfield and we have a clear idea of what we have to do - score twice," Raul told The Times.
"The other day we were hit strongly by the defeat, but we know we are going to have our chances and we are not going to give up."
Los Merengues had a sloppy first part of the season, where coach Bernd Schuster was replaced by Juande Ramos after a horrible run of poor domestic results.
However, Raul is convinced that Ramos, who's unbeaten in eleven Liga games with Real, can lead the club to an away win over Rafa Benitez's Liverpool.
"At the beginning of the season we had a lot of problems - we were scoring goals, but letting them in as well and that cost us a lot of points," added the 31-year-old.
"Since the arrival of Ramos we are more disciplined. We are now in good shape, above all physically and mentally."