West Ham are "massive", according to a popular fan chant, but Olympique Lyonnais president Jean-Michel Aulas does not appear to agree.
Lyon sold Brazilian playmaker Lucas Paqueta to the Hammers this week.
West Ham paid an initial transfer fee of £36.5 million but Lyon could eventually receive over £50m including add-ons, as reported by BBC Sport.
Paqueta made it clear earlier this summer that he wished to leave Lyon but Aulas was surprised to see the player end up at the London Stadium, rather than somewhere more prestigious.
"It is unfortunate that Lucas Paqueta is leaving. But he wanted to leave," Aulas told Canal+ on Monday.
"We thought we'd have very big clubs come in, but we didn't have them. We then were forced to speak at the last minute with West Ham."
Paqueta, who scored 18 goals and provided 11 assists in Ligue 1 over the past two seasons, had been linked with interest from both Newcastle and Arsenal, but neither club approached Lyon with a formal bid.
West Ham have not won a major trophy since lifting the FA Cup in 1980.
But they reached the semi-finals of the UEFA Europa League last season and have the fourth biggest stadium in the Premier League in terms of its capacity.
The Hammers will play in the UEFA Europa Conference League this season. They have been drawn in Group B alongside FCSB, Anderlecht, Silkeborg.