The Red Devils secured safe passage to the last 16 with a 3-1 win over Braga in Portugal on Wednesday night, a result which maintained their 100 per cent record in Group H.
And the 70-year-old, who guided the Old Trafford side to their second and third wins in the competition, is now keen to match the Reds' five European Cup victories.
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“In terms of the history of our club, we should have won more and I want to win it again and get into the bracket of winners like Liverpool, our biggest rivals, Bayern Munich and Ajax," the Scot told reporters.
“AC Milan and Real Madrid have got separated from the rest but that definitely drives me on a bit.”
Despite his past success in Europe's premier cup competition, Sir Alex still rues the final defeats at the hands of Barcelona in 2009 and 2011.
“I get really frustrated when I think about the opportunities we have had to win it, but you can’t be greedy,” he continued.
“You look at my career and I have won two European Cups and the Cup-winners’ Cup and I am proud of that.”