The council's planning committee was looking at amended plans from Sainsbury's for 12 two-bedroom flats, six two-bedroom houses and six three-bedroom houses, together with a toddlers' play area, on land previously reserved for a possible link road.
Members said they had no objection to the plan providing Sainsbury's gave a contribution big enough to cover the cost of an additional classroom at the school.
Committee chairman Anna James told The Herald: "The infant school is full and 24 more houses in Liphook will mean a lot more children.
"There doesn't seem to have been a substantial contribution from the 120 executive houses already built and there is a shortage of school places.
"If the number of houses is increasing again in the village, we need a contribution."
Mrs James said the parish council could not object to the plan on the grounds that the land should be reserved for the link road.
The county council highways department, she said, had accepted Sainsbury's traffic assessment which claimed there was no need for a link road.
The planning application will be decided by East Hampshire District Council.