Uefa advanced its assessment date to 1 March rather than June, but the Cas panel found that this change had been properly communicated by Uefa and that Drogheda ought to have known about it.
A majority of the panel also rejected Drogheda’s submissions on alleged unequal treatment by Uefa.
Drogheda, who are currently third in the League of Ireland Premier Division and face Shamrock Rovers on Monday night, also called the decision “unjust”.
“Rules should protect opportunity, not prevent it,” their statement added.
“Especially for community-driven clubs like ours who fight every day to punch above their weight.
“Nevertheless, we accept responsibility. And we’re sorry. But while we are saddened, we are also emboldened.
“We will not let this setback define us. Instead, we will use it as fuel. Our club has never been handed anything and we’ve earned every inch through grit, resilience, and unity. And we will continue to do so.”
Derry City, who Drogheda beat in the FAI Cup final, are unable to join Shamrock Rovers and St Patrick’s Athletic in the competition as the deadline for a Uefa licence has passed.
Drogheda’s sitaution is similar to that being experienced by Crystal Palace, who qualified for the Europa League by winning the FA Cup in May.
It is the only time the Premier League club has qualified for European football in their 120-year history, but Uefa is set to decide whether they breached its rules on teams under one multi-club ownership structure competing in that competition.
Uefa’s final ruling will centre on American businessman John Textor, owner of Eagle Football – which holds a 43% stake in Palace.
Eagle Football also owns a 77% stake in French side Lyon, who – like Palace – have qualified for next season’s Europa League.
In recent seasons, Aston Villa, Manchester City and Manchester United have all been admitted into European competition despite initial concerns over multi-club ownership.