There's a good reason to believe his daughter was not sacrificed as in "killed" but that she was given and dedicated to God as a eunuch for the Kingdom since she would spend her whole life in service to God instead of married and spending much of her time meeting the needs of her family. God's people knew/know that He expects people to keep their word. Promises/oaths/vows are to be kept and taken seriously. Numbers 30 is an entire chapter dedicated to when vows can be broken, and that was only if a husband disallowed his wife's vow or father disallowed his daughter's vow on the day he heard it. Ecclesiates 5:4-6 talks of the seriousness of the vow. We're not to make promises before or to God and then say "oops, it was an error".
When we read Judges 11:37-38, the daughter is asking to "bewail her virginity" with her friends for two months instead of asking to spend the last two months of her life doing something else. Verse 39 says she returned so Jephthah could keep his vow, "and she knew no man". She remained a virgin for the rest of her life (never got married). Verse 40 says the daughters of Israel went to lament her every year for 4 days. This doesn't suggest they mourned her 4 days every year, especially since God tells us not to communicate with the dead and allowed Israel only a month to mourn Moses before Joshua took leadership. It suggests they had a yearly get-together.
Jephthah cut off his lineage and denied his daughter the opportunity to have a family by making his vow, but it's highly improbable that she was killed because the Lord detests child sacrifice.