Moyes was appointed Old Trafford boss after Sir Alex’s 26-year reign ended last season and will make his bow in Europe’s elite club competition against Bayer Leverkusen on Tuesday.
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"After the draw, I phoned Sir Alex to talk about it and he said he thinks it’s one of the hardest draws United have ever had in the Champions League," Moyes said.
"If that’s coming from him, then it must be tough.
"There are some great squads but I do think that on any given day we would fancy our chances. We hope to get those opportunities to prove that we are good enough to beat them.
"I’ve got to make sure we’re in the Champions League this year, next year and the years after, and competing to try to win it."
Sir Alex was in the stands for the first time since stepping down from the hotseat during United’s 2-0 Premier League win over Crystal Palace on Saturday.