The Red Devils went through thanks to a Robin van Persie hat-trick to bounce back from their humiliating defeat at home to Liverpool on Sunday.
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"Depending how the draw goes but we will go in as underdogs for a lot of matches," he replied when asked by the press if they could lift the trophy, "but I genuinely believe this football club is capable of it.
"If we play to our capabilities, which we have not done enough, we can be a match for any team.
"I don't want to come out and say 'this is the moment' but I really hope it is."
Moyes praised his side for the victory over the Greek champions, enthusing: "It was a magnificent team performance. We carried no passengers. Everybody fought their corner and I thought we played well. We played good football.
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The United boss also reserved praise for Ryan Giggs after the Welshman delivered a sublime performance in midfield.
The veteran, who has been rumoured as a potential short-term replacement for Moyes in recent weeks, had not started a match since January 7 prior to the win over Michel's side.
"His two passes made two of the goals. His passing was fantastic and his all-round play was fantastic. He defies his age. He's a great player," said Moyes.
"He is 40 years old and I need to be looking to the future. I'm trying to give everyone opportunities. Tactically I needed him to play a certain role which he knew and he understands. He carried that out with his assists for the goals."