Ögedei didn't even tried to take Europe, it was a really big scout party which casually obliterated every army they encountered, arrived at Hungary, seen the pushta and considered staying because it reminded them of home and then went back because khan died and new one had to be elected. In the meantime collective Europe was thrown into a state of abject terror not known since Attila the Hun. But of course as soon as it passed, islamophobia kicked in, they started to blabber about Prester John and tried to use Mongols against muslims.