I think shoegaze relates more to the use of effects pedals and whammy bar/tremolo arm, but even then psych artists throughout the ages have always encorporated new age effects to spice up their sound. the guitarist of the kinks did the tremolo arm thing while playing on do you know walter in 68 way before Kevin shields. Shields has said that the kinks were a huge inspiration and also the cover of loveless is a homage to the kinks kontroversy album cover
tldr; shoegaze should be considered neo psych