The Matildas were dumped out by England in the semi-finals after losing 3-1 to Sarina Wiegman's rampant side.
Sam Kerr gave the hosts hope in the second half after scoring one of the goals of the tournament to level the game up at Sydney's Stadium Australia.
But England hit back through Lauren Hemp and new Gunner Alessia Russo to seal their place in Sunday's final against Spain.
Arsenal duo Catley and Foord - along with the rest of their teammates - were left devastated as England celebrated reaching back-to-back major finals.
The Gunners were quick to try and console the pair as they congratulated the two on an incredible tournament where they helped create history.
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Catley and Foord were instrumental in Tony Gustavsson's side reaching the last four - the first time that Australia have progressed into the World Cup semi-final.
A tweet from Arsenal's Twitter account read: "Captured the hearts of a nation and fought until the very end.
"You've done your country proud, Steph Catley and Caitlin Foord."
Replying to the post, their Arsenal teammate Katie McCabe, who played against the pair in the World Cup opener which saw Catley score the winner, commented two love heart emojis.
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Fans were also loving Arsenal's wholesome message, as one supporter said: "Hold your heads up, we're so proud of you."
Another remarked: "Legends y'all are! What a terrific tournament y'all have had... we couldn't be more proud of y'all..."
A third added: "Hold your head high ladies, you've done your nation proud."
This fan then tweeted: "Gave it absolutely everything, could not be prouder of these two. Both have been fantastic in this World Cup."
One Gooner then posted: "Proud of our Arsenal girls today. Steph and Caitlin, you've been great the whole competition."
Meanwhile another simply stated: "They've done great, hold your heads high."