Well, since Christ quoted the Septuagint directly numerous times, that, as they say, is good enough for me!
The Gospels were written in Greek, but it is likely that Jesus Christ spoke in Aramaic and Hebrew. Both Christ and the authors of the Epistles cited Old Testament sources that resemble Septuagint and Masoretic quotations. There is also the possibility that there were alternate Hebrew texts, based on information from the Dead Sea Scrolls, one of which was the basis for the Septuagint and the other becoming the Masoretic text. It is thus possible that Christ, though speaking in Aramaic or Hebrew, cited a Old Testament source from which the Septuagint derived.
While the early church generally championed the Septuagint against the Masoretic text, it must be remembered that Jerome used the Hebrew Masoretic text to translate much of the Old Testament (Psalms and the Wisdom books excepted) into Latin.