I love the Beatles, their influence will forever be felt in music. And their psychedelic tracks (especially the deep psychedelic Eastern-influenced sound) are some of the best in their discography.
---BUT... If you guys are really going to bring up the origins of psychedelic rock, you have to look to the 13th Floor Elevators.
Moving Sidewalks, too. And a million other bands...
I don't think I'd say "Tomorrow Never Knows" started the psych movement, but probably popularized it. Kinda like Radiohead and combining electronic music & rock...they didn't invent it (not even close!), but they took it to the mainstream.
You guys will probably like this band too (more from Kevin Parker / the Perth scene):