The Andalusian side continued their remarkable debut campaign in Europe's elite club competition by overturning a 1-0 first-leg deficit against Porto with a 2-0 home win in Wednesday night's return meeting.
Isco's 43rd-minute goal levelled up the scores on aggregate and, after Porto had lost Steven Defour to a red card just after half-time, Malaga substitute Roque Santa Cruz struck what would prove to be the decisive goal 13 minutes from time.
Pellegrini, who led unfancied Villarreal to the semi-finals of the Champions League in 2006, believes his side thoroughly deserve their place in the last eight and hopes to avoid being paired with either Barcelona or Real Madrid in Friday's draw.
The former Madrid coach told reporters: "The ideal thing would be to not play against the Spanish teams. But you face who you face, and whoever we play we will try and have a good tie."
The other five teams to have got through to the quarter-finals are Bayern Munich, Borussia Dortmund, Galatasaray, Juventus and Paris St Germain.
On the win over Porto, Pellegrini added: "We went out there with a cool head and maintained our focus to ensure we didn't concede a goal.
"The first 15 minutes of play was a bit tense, but we were the superior side for the remainder of the match and definitely deserved to win.
"Porto are one of the best teams in Europe and we knocked them out of the competition.
If we are eliminated in the future, then we'll make sure we go down fighting."