The Roar confirmed on Wednesday that D'Agostino would miss six weeks with a knee injury suffered against Perth Glory on Saturday.
It certainly rules the 28-year-old out of internationals against Cameroon at Sydney's Accor Stadium on March 27 and Curacao at Melbourne's AAMI Park four days later.
Red-hot Toure (groin) and D'Agostino are the most recent additions to a long injury list.
Uncapped Noah Botic (broken ankle) is out of contention while defender Lewis Miller will miss the World Cup with a ruptured achilles tendon.
Harry Souttar, Craig Goodwin and Cammy Devlin are also sidelined.
The injury also harms D'Agostino's own hopes of auditioning to make Australia's squad for the tournament in June - having returned to the A-League Men on loan from Norwegian club Viking with that goal.
Veteran Macarthur FC striker Mitch Duke looms large among the options to lead the line in March, while versatile Melbourne Victory attacker Nishan Velupillay is a Popovic favourite.
Japan-based brothers Tete and Kusini Yengi, untested Dundee striker Zac Sapsford, Perth skipper Adam Taggart and uncapped Poland-based Deni Juric are other options.
Hibernian striker Ante Suto, eligible for both Australia and Croatia, has had contact with the Socceroos and could be a smoky.
Elsewhere, forgotten goalkeeper Joe Gauci reignited his own bid for World Cup selection by helping Port Vale into the English FA Cup last 16.
Gauci kept a clean sheet in a 1-0 victory as former Wellington Phoenix star Ben Waine's extra-time goal eliminated Championship side Bristol City.
The South Australian goalkeeper, who is on loan from Aston Villa, started matches in Popovic's first window as coach but has fallen out of favour and been left out of recent squads behind Mat Ryan, Paul Izzo and Patrick Beach.
But Gauci, 25, has started 20 games for Port Vale and will take confidence from a four-game unbeaten run.
The League One strugglers' first fifth-round appearance in 30 years was sealed after New Zealand-born Waine, whose family hail from Newcastle, scored the only goal after 112 minutes, rounding keeper Joe Lumley and netting from a tight angle.
Gauci was rarely tested as City, who made eight changes to their previous Championship line-up, managed only a Tomi Horvat free kick on target.
