The Premier League champions were handed a favourable tie in the round of 16 in the form of Greek outfit Olympiacos, while Arsenal and Manchester City face testing encounters with Bayern Munich and Barcelona respectively.
United finished top of their pool, while City and Arsenal had to settle for runners-up berths, meaning the Premier League duo were not among the top seeds for the knockout phase.
Alexander is now confident of reaching the quarter-finals, and is counting on a big United following in Greece to help their cause.
"If you look at the ties Arsenal and City got, that shows why you have got to win the group," he said.
"Whoever came out of the pot would have been a good one to draw.
"United are a big club in Greece so we will have a good following over there."
United are looking to do better than their effort last season when they were knocked out in the last-16 stage with a 3-2 aggregate defeat to Real Madrid.
