"Not Over Yet" was met with critical acclaim from music critics. Scottish
Aberdeen Press and Journal described the song as "uplifting".
AllMusic editor Michael Gallucci felt that it "makes any sort of lasting impression".
J.D. Considine from
The Baltimore Sun remarked in his review of
If I Could Fly, "But rather than try to make the listener dance, as so many divas do, Grace would rather entice us — and there's something wonderfully inviting about that."
Larry Flick from
Billboard magazine wrote, "Grace has it all—a highly videogenic image, an angelic voice, and the ability to write material that deftly straddles commercial viability and underground hipness. She has already wooed punters in her native
U.K. with this silky slice of
trance/
disco, and early reaction from tastemaking radio-programmers hints that even greater stateside success is on the horizon." In his weekly UK chart commentary,
James Masterton viewed it as "another dance hit from the
Perfecto stable, wildly commercial and sending clubgoers wild the country over". Later, writing for
Dotmusic, he felt it is "easily one of the best dance hits of the year so far".
Mixmag named it Single of the Week, adding, "Quite simply the best record I have heard in months. Vibrant, passionate and ultimately spiritual." Pan-European magazine
Music & Media commented, "Not over yet? No way, it's only just beginning, the renewed appreciation of synth or
electro pop—of course in a fashionable new dance coat. The girl sings gracefully in a sea of sequencers."
James Hamilton from
Music Week's
RM Dance Update called it a "sweetly cooed commercial
techno scamperer" and a "haunting sweet girl cooed and fluttery synth chugged attractive simple burbling old raver".
Iestyn George from
NME praised it as an "epic soundscape of uplifting
deep-house". He added, "This is dance music in widescreen
with surround sound — plaintive vocal melody, lush piano sounds, crisp percussion, minimalistic trance interludes and random whale noises for all
the Orb fans in the, er, house. A contender for single of the year so far? You betcha." ==Chart performance==