The Ligue 1 outfit left the Emirates in the first leg last 16 tie with a 3-1 win, despite the Gunners being heavily tipped to ease to victory.
However, Allardyce believes Monaco’s impressive defensive record going into the fixture meant they were far from the underdogs.
The Hammers travel to the Emirates on Saturday (3pm), but Allardyce believes his side lacks the quality to emulate Monaco’s triumph.
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Sam Allardyce admires Monaco's defensive record this term
Monaco have been extremely good at not conceding goals
Sam Allardyce
The Upton Park manager said: “In terms of Monaco, we haven’t got the quality of players they’ve got. I think that’s the first and foremost.
“Monaco have been what we haven’t this year, and that’s being extremely good at not conceding goals.
“Everybody thought that it was an easy tie, but it wasn’t when you look at their defensive record. I think when they played, they had only conceded one goal in the last 11 games.”
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