מצודת דוד על שמואל א א:יב-יג
שומר את פיה: רוצה לומר: היה מסתכל לשמור מוצא שפתיה, לשמוע מדבריה וחנה אבל חנה היתה מדברת על לבה, רוצה לומר בלחש, כאלו מדברת אל לבה, ולא היה נשמע לעלי ויחשבה עלי לשכרה כי כן דרך השכור לנענע בשפתיו ואין אומר ואין דברים
Metzudat David on I Samuel 1:12-13
Watching her mouth: It means to say, he was looking to watch what came out of her mouth, to hear her words and Chana was speaking her heart, which is a way of saying silently, as though she were speaking to her heart, and her words were not heard by Eli and he thought her a drunkard because this is the way of the drunkard, to move his lips and not to actually say anything
ותען חנה ותאמר לא אדני אמר עולא ואיתימא רבי יוסי ברבי חנינא אמרה ליה לא אדון אתה בדבר זה ולא רוח הקודש שורה עליך שאתה חושדני בדבר זה איכא דאמרי הכי אמרה ליה לא אדון אתה לאו איכא שכינה ורוח הקודש גבך שדנתני לכף חובה ולא דנתני לכף זכות מי לא ידעת דאשה קשת רוח אנכי
"And Hannah answered and said, No, my lord" (ibid. v. 15) — 'Ulla (another version: R. Jose b. R. Hannina) declared : She said to Eli, "Thou art not 'a lord' in this affair, nor does the Holy Spirit rest upon thee, seeing thou hast suspected me of this thing." Some declare that she spoke to him thus : "Thou art not a lord ; neither the Shekinah nor the Holy Spirit is with thee, for thou hast judged me in the scale of guilt and not in the scale of merit[4]. Dost thou not know 'I am a woman of sorrowful spirit'?"
The Family Midrash Says: The Book of Shmuel 1, page 24
The Vilna Gaon explains that Eli had a reason [for not judging Chana favorably].
He asked Hashem through the Urim Vetumim to explain her strange behavior. The following letters lit up on the choshen mishpat [breastplate]: הכרש.
Eli needed ruach hakodesh [divine inspiration] to combine the letters correctly in order to know the answer. He understood the answer to be שכרה/ a drunken woman. He was sure that this was the correct answer and therefore told Chana very definitely that she was drunk.
But Chana replied, "You have no ruach hakodesh; you didn't assemble the letters correctly." The real answer was כשרה, like Sara, meaning this is a childless woman like (our mother) Sara.