The Australian Test star claimed four for 23 but was unable to prevent Gloucestershire reaching 157 for seven to pass Hampshire's total of 154.
Opener Craig Spearman set up victory with a quickfire 50 - 46 runs coming from boundaries - before he was bowled by Alan Mullally (three for 29).
Warne then helped reduce the hosts to 137 for seven, but Shoaib Malik (32) saw Gloucestershire home.
Only tailenders Dimitri Mascarenhas (52) and Chris Tremlett (24) provided any resistance during Hampshire's innings, putting on 60 for the ninth wicket.
Both players fell victim to Mark Alleyne (three for 25) but Jonathan Lewis led the Gloucestershire attack, returning four for 39 from his 10 overs.