The MK Dons midfielder, on loan from Aston Villa, saw his match ended after two bookable offences in Sligo, where Moritz Leitner and Philipp Hofmann scored either side of a Kevin Volland brace.
It was a result that had looked likely from the start of the European Championship qualifier at the Showgrounds.
Noel King's side fell behind after just 12 minutes when Leitner's strike from the edge of the box beat goalkeeper Aaron McCarey.
Jonas Hofmann came close to extending the visitors' lead, before Sean Murray was denied by Marc-Andre ter Stegen at the other end.
Carruthers also came close with a volley, only for Germany to soon pull further ahead.
Volland nodded home in the 22nd minute to double their advantage, with the Hoffenheim striker heading home another two minutes later.
Connor Smith forced ter Stegen into a fine save as Ireland looked to reduce the deficit, but any chance of a comeback was dealt a major blow when Carruthers was given a second yellow card for a foul on Leonardo Bittencourt in the 61st minute.
Ireland's resilience was broken again with six minutes remaining through substitute Hofmann, although Shane Duffy, Smith and Graham Burke all had late efforts of note.