The Israelites said Shirah on seeing the wicked Egyptians drowning.
Did Noah act in a similar way, praising God for saving him and his immediate family and seeing millions of wicked humans drowning in (boiling?) flood?
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Noach did not say Shira when they drowned.
The Malochim were criticized for saying Shira when the Egyptians were drowning.
Klal Yisroel was not criticized because the Egyptians had been their tormenters who had been running after them so they were also thanking Hashem over their salvation.Noach was not being chased after by the people of his generation.
Chazal discuss the opposite question. Why didn't Noach daven for his generation? He is even criticized by them not having done so. But he clearly didn't say Shira upon their destruction.
On the contrary. Rav Chaim Friedlander זצ"ל in his שפתי חיים על פרשת נח, brings from the זוהר (השמטות בראשית רנד) that when נח came out of the תיבה and saw the destruction, he cried out to ד' asking why He hadn't had mercy on the people
כשיצא מן התיבה וראה את העולם חרב והתחיל לבכות לפניו ואמר רבש"ע נקראת רחום, היה לך לרחם על בריותיך! השיבו הקב"ה ואמר רעיא שטיא, השתא אמרת דא? למה לא אמרת בשעתא דאמרית לך כי אותך ראיתי צדיק לפני וכו ואח"כ עשה לך תבת עצי גופר וכו לא עאל בלבך למבעי רחמין על ישובא עלמא?
On the other hand, Rav Dovid Kviat זצ"ל in his סוכת דוד suggests, in order to explain a מדרש, that the קרבן which נח brought after the מבול was not just to thank G'd for saving him, but also out of recognition that everything G'd does is fair, even a destruction brought about by Him.
There is a machlokess if the tzohar is a window or a precious jewel. The darshanim say as follows: There is also a machlokess if tamim haya be'dorosav means that only in his generation, but had he been in the generation of Avraham then he would have been considered as naught. Others say that all the more so had he been in the generation of Avraham he would have been considered to be a great man. The darshanim say that according to the opinion that he was truly great, then he was allowed to see the downfall of his generation and the tzohar was a window. However if you say he was not truly great then the tzohar was a jewel, as he was not allowed to look out at the downfall of his generation.
I don't think that either way he would have said shirah, as per @Schmerel.