It has been said that in some ways Evangelion is Anno's critique to what he saw as wrong with the mecha anime genre of the time. Lists of shows that Evangelion has influenced abound, but what were the titles that Anno was critiquing?
http://www.animenewsnetwork.com/feature/2002-06-11 Anno is not really critique anything in particular. He came up with the concept of EVA when he was going through depression. It is a coming of age story and offers ideas of living the life that he and Gainax thought were important for life. The show does play homage to series like Ultraman; and is littered with hidden references. Most of the food in the vending machines were discontinued favorites that the animators liked (the junk food market has a quick turn around with many flavor varieties being limited edition).
I would recommend watching Blue Blazes (Aoi Honō). This J-drama has Anno and other members of Gainax and does show a little about who Anno is and how Gainax made the Daicon (Diacon 4 in particular) opening that made them famous.
I would look at ME! ME! ME! This recent music video is a much straight forward critique on how anime is consumed by Otakus in Japan.
Otaku no Video is another cool OVA to check out. Made by Gainax it is something of an autobiography into how the studio was created.