Hamble boss Larry Clay said he was "gutted" after Steve McNulty's 90th-minute decider had given Andover a 2-1 success.
"It was a good end-to end-match," he said.
"I thought we were worth a point, but their second goal was on the cards because they really attacked us in the last 15 minutes."
Danny Sullivan had given Andover a 26th-minute lead, capitalising on a Hamble defensive mix-up, only for Rob Ackroyd to level with a 30-yard drive from a free-kick in the 63rd minute.
Hamble thought they should have had a penalty in the second half when Joe Partridge was fouled. "It was blatant," said Clay, "but typical of our luck."
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