[3] Production of the released track was credited to Nick Lowe, even though the demo session was entirely the work of Costello as both artist and producer.

!, following "I Can't Stand Up for Falling Down" and "High Fidelity", though, unlike these previous singles, "New Amsterdam" was released as part of an EP.

[6] The other songs included on the EP were "Dr. Luther's Assistant" (a leftover from This Year's Model), "Ghost Train" (which originated from a lyric Costello wrote in 1972), and "Just a Memory" (which was written for Dusty Springfield).

[9] AllMusic's Stephen Thomas Erlewine named it a "full-fledged masterpiece", while the same site's Stewart Mason characterized it as a "simple but beautifully effective song".

"[12] Record World called it a "stark and powerful ballad" in which "Costello doesn't waste a word or an emotion.

"[13] Jim Beviglia of American Songwriter named the song Costello's fifteenth best, praising its "dreamy, melancholic vibe" and noting that "anyone who has ever felt like they have no connection to the comforts of home can appreciate 'New Amsterdam,' a lovely place to visit vicariously via Elvis' pretty song even though you would never want to live there".

[6] Beginning with the tour supporting his 1989 album Spike, Costello has sometimes performed "New Amsterdam" in a medley with a cover of the Beatles' "You've Got to Hide Your Love Away".