You are correct in that the entire transaction will be rolled back. You should issue the command to roll it back.
You can wrap this in a TRY CATCH
block as follows
BEGIN TRY
BEGIN TRANSACTION
INSERT INTO myTable (myColumns ...) VALUES (myValues ...);
INSERT INTO myTable (myColumns ...) VALUES (myValues ...);
INSERT INTO myTable (myColumns ...) VALUES (myValues ...);
COMMIT TRAN -- Transaction Success!
END TRY
BEGIN CATCH
IF @@TRANCOUNT > 0
ROLLBACK TRAN --RollBack in case of Error
-- you can Raise ERROR with RAISEERROR() Statement including the details of the exception
RAISERROR(ERROR_MESSAGE(), ERROR_SEVERITY(), 1)
END CATCH