See 1 Samuel 1:2 and note. She means that wine was not the cause of her present discomposure, but grief of heart.
Related Commentaries of 1 Samuel 1:15
1 Samuel 1:15
15 And Hannah answered and said, No, my lord, I am a woman of a sorrowfulg spirit: I have drunk neither wine nor strong drink, but have poured out my soul before the LORD.