In a critical manner; with, or in terms of, criticism.
"The reviewer discussed the film critically, focusing heavily on its weak character development rather than praising its visual effects."
In plain English: Critically means analyzing something very carefully to judge its quality or importance.
"The teacher criticized him critically for his poor attendance."
Usage: Use critically to describe an evaluation that analyzes something carefully and points out flaws rather than simply judging it harshly. This distinguishes the word from using "critically" as a synonym for "severely," which implies extreme intensity without necessarily involving detailed analysis.
The word comes from the adjective critical, which itself derives from Latin meaning "able to judge." It entered English with that sense of judgment and was later adapted by adding -ly to form an adverb describing a manner of analysis or importance.