"From the beginning we were on top of Madrid and we didn't allow them to play," he said.
"We are happy after that result. We know it will be really difficult to play United but we have to try to play in the same way we played on Tuesday.
"We played very well [against Real]. Fernando Torres was unbelievable and hopefully on Saturday he can be the same.
"If we play like that in all the games, it will be difficult for any team to beat us."
Mascherano believes the club's form in Europe - they have not lost in 10 matches (including qualifiers) this season - has lifted everyone's confidence.
Victory over Real saw Liverpool progress to the quarter-finals of the Champions League for the fourth time in the last five years, having won the competition in 2005 and finished runners-up in 2007.
"In the last two or three years we have been playing against top sides and we have proved we can beat them," he said.
"We are in the quarter-finals so the teams are really good but we know, if we play like we did against Madrid, we can beat anyone."