Everett was impressed by Lincoln's speech.
Everett was a very popular speaker and noted official:
https://en.wikipedia.org/wiki/Edward_Everett#Teacher,_writer,_and_speaker
Everett took up his teaching duties later in 1819, hoping to implant the scholarly methods of Germany at Harvard and bring a generally wider appreciation of German literature and culture to the United States. For his Greek class he translated Philipp Karl Buttmann's Greek lexicon. Among his students were future Speaker of U.S. House of Representatives Robert Charles Winthrop, presidential son and future U.S. Representative Charles Francis Adams, and future philosopher and essayist Ralph Waldo Emerson. Emerson had first heard Everett speak at the Brattle Street Church, and idolized him. He wrote that Everett's voice was "of such rich tones, such precise and perfect utterance, that, although slightly nasal, it was the most mellow and beautiful and correct of all instruments of the time."
In 1820 Everett was elected a Fellow of the American Academy of Arts and Sciences. That year he became editor of the North American Review, a literary magazine to which he had contributed articles while studying in Europe. In addition to editing he made numerous contributions to the magazine, which flourished during his tenure and reached a nationwide audience. He was also instrumental in expanding Harvard's collections of German language works, including grammars, lexicons, and a twenty-volume edition of the collected works of Johann Wolfgang von Goethe, whom Everett had visited in Weimar and whose works he championed on the pages of the Review.
Although Everett was renowned as a speaker and although his address was the kind that American audiences of the time appreciated, he recognized in Lincoln's speech the qualities of a truly "great work": "I should be glad," he wrote Lincoln, "if I could flatter myself that I came as near to the central idea of the occasion, in two hours, as you did in two minutes" (Everett to Lincoln, 20 Nov. 1863).
https://history.hanover.edu/courses/excerpts/121everett.html
After his speech at Gettysburg, Lincoln confided to a companion and to Everett that he considered his two minute address to be a failure.
Contrast this with the attitude of today's president-elect who probably would characterize both Lincoln and Everett as "losers" were they alive today. Somewhere in the skills of diplomacy loyalty and leadership and qualities of honor and integrity, humility is one I look for.