Adding onto the other answer, the exact thing that gets interpreted as an EVA reference is Senjougahara's line:
You won't die. [Short break.] You won't die. Because I'll protect you.
It is clear that this is probably the content of the "reference", as Araragi makes the comment about wanting "no unnecessary Evangelion references" right after this line.
This is nearly identical to a line between Shinji and Rei in episode 6 of the EVA anime, as mivilar has pointed out. In that episode, there is an Angel attacking NERV, which has so far repelled the attacks against it. The solution is to use a very high-power rifle against the Angel from a distance, with Rei acting as a back-up or shield for Shinji.
Prior to the start of the mission, Shinji is worried, and asks Rei if she is scared. In response, she tells him that he shouldn't be scared, that "you won't die; I'll protect you." (The exact wording probably depends on the subtitle set.)
Aside: Naturally, this suggests that the EVA line is rather notable (something which did not occur to me when I first watched EVA). I would suspect that it has become so partly because of the pacing of the specific scene. Perhaps it's also easier to catch the mirroring of words in Japanese, as this is not a line with very idiosyncratic vocabulary. (Compare to Senjougahara's reference to Fullmetal Alchemist in Bakemonogatari, where the exact ordering or wording of "X kilos of A, Y grams of B, . . ." doesn't matter too much in terms of the ability of a watcher to catch the reference.)