The resolution was passed on Wednesday night with 120 votes in favor, 8 votes against and 45 abstentions.
At least 129 Palestinians have been killed by Israeli fire in protests near the border with Gaza in recent months.
The Arab-backed resolution condemns Israel's use of "excessive and disproportionate" force against Palestinian civilians and calls for protection measures for Palestinians in Gaza and the occupied West Bank.
"Civilian victims are unacceptable and while calling on Israel not to use excessive force, we understand that Israel has the right to self-defense," Linkevičius told BNS on Thursday.
"In assessing actions, we have to place certain responsibility onto Hamas and other terrorist groups, because they use women and children as a shield for their provocations," the minister said.
"This resolution is unbalanced and won't contribute to stability. By giving no assessment to Hamas' provocative actions, we make a mistake, and we can't back such a resolution," he added.
Linkevičius said that he had discussed this position with Turkey's foreign minister by phone on the eve of the UN vote.
Twelve 12 EU countries backed the non-binding resolution, but 16 abstained.