Kevin James set Lymington on their way to a 2-0 home victory over lowly Alton with a goal in the first minute.
He later missed a penalty in the second half before Paddy James added a second.
Linnets boss Ian Robinson said: "We should have won by more."
And he added that it would be nice to see bigger attendances.
"You put a lot of hard work in but the people here don't seem to appreciate it," he confessed.
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