Jesus understood Daniel's prophesy as being unfulfilled in his day. Though he would have been well-familiar with Antiochus Epiphanes and the Maccabees, he treated Daniel’s words as not yet having been fulfilled. Therefore, the abomination Daniel was speaking about was not accomplished (at least with any finality) by Antiochus placing an idol of Zeus in the Temple and sacrificing a pig on the Jewish altar. It certainly seems to be a picture of things to come, but it wasn’t the intended, ultimate fulfillment.
Furthermore, Daniel specifically says that the abomination comes midway through a covenantal arrangement with, presumably, the pompous little horn. There was no such instrument with Antiochus Epiphanes, nor was there any with the Romans in the 60's. So Daniel was not referring to Antiochus when prophesying this, and Jesus did not envision Titus (Emperor Vespasian/General Titus) when citing it. What Daniel spoke of is not an incursion and destruction (as in the case of the Romans), but a cessation of proper sacrifice and a substitution of detestable (unclean) things.
“Wing” (Hebrew: kanaph=wing, covering), as is translated in some English versions, in this part of Daniel is nonsensical, though wing is often a perfectly good translation when this word is used. Its range of meaning extends from edge or corner to covering, and it is the latter that makes sense in this context. Besides, for “wing” to be intended, translators (e.g. NIV following the LXX and Theodotion) must add the phrase “of the Temple” which is not in the Hebrew at all—not even a hint! The Abomination does cover or overspread the Temple, figuratively, which makes perfect sense in light of Revelation 13:15.
Jesus said that the abomination will stand in the holy space. In Rome’s destruction (really, obliteration) of Jerusalem nothing stood--literally, the Romans threw everything down and stood up nothing. That kind of destruction was actually prophesied by Daniel (9:26) as having already occurred when the Abomination takes place, really, as something parenthetical to the cutting off of the Messiah. So Rome's destruction of Jerusalem in 70 CE is prophesied by Daniel, just not as part of the Abomination of Desolation.