The Reds failed to progress from the group stages in 2011/12 after losing in Basel in the final fixture but there is a real determination to put things right - starting with Wednesday's home match against Galatasaray. Sir Alex clearly remains focused on trying to land a fourth European Cup for the club.
"We've had opportunities in the competition," he stated. "We've lost two finals to Barcelona and won two in the last decade or so but we want to do better. Certainly, we'll do better than last year - no question about that.
"The European Cup is incredible. There's an atmosphere in the build-up to a European final and great charisma about it. Also, without question, it elevates your status within the game like the Real Madrids and AC Milans. We want to be up there in terms of the number of trophies won in European football."
When asked if the standard of some of the perceived lesser lights in the Champions League has improved recently, the manager replied: "We've seen some examples of that over the last few years. For instance, the Cypriot team [Apoel Nicosia] getting to the quarter-finals and Basel beating us and getting to the next stage against Bayern Munich.
"There are a couple of other examples of the lesser-known teams doing well and Monaco played Porto in the final one time, which was a surprise. But, at the end of the day, you always think one of the big ones is going to win it.
"It doesn't do the competition any harm, to be honest with you and who would have predicted Chelsea winning it last season?