Robbers & Cowards received generally positive reviews from music critics who were impressed with the band's blues rock sound and lyrics that told morose tales of yesteryear. Joe Tacopino of PopMatters praised the tracks for their production and mature storytelling, calling the album "more subtle and honest than Jack White’s various projects." He concluded with, "These ambitious youngsters are definitely worth the trip, even without the ostentatious vocal harmonies." Despite finding the album a bit rushed and an amalgam of their previous EPs, Jeff Weiss of Stylus Magazine said that there's potential in the band from the first three singles concluding with, "It’s a good debut, maybe even a very good one. Whether or not this band will achieve greatness remains anybody’s guess." Chad Grischow of IGN praised the tightly crafted production for sounding crisp yet cluttered and the tracks for conveying various introspective topics concluding with, "The depth of the music, topics, and lyrics is something that most bands spend years trying to pull together, but Cold War Kids pull it off on their debut with ease." Betty Clarke of The Guardian commented on how the religious overtones in the songs can get tiring when Nathan Willett shouts about "murder and alcoholism that both sound like a tempting escape." But Clarke concluded by saying the band can still write great songs and Willett performs better sounding like Jeff Buckley than Jack White.
The album did received some negative reception. Joe Crofton of musicOMH called the album a mixed bag, saying that it loses momentum after the first two tracks and drags towards its conclusion. He commented that the influence of the Internet on the indie scene may have lessen the album concluding with, "That isn't to say that this is a bad album but it definitely doesn't deserve the headache inducing amount of hype that has surrounded it." Sam Richards of Uncut found songs like "We Used to Vacation" and "Hang Me Up to Dry" showcased the band's "real gift for drama," but criticized the rest of the album for its misplaced blues production and sense of detachment from the songs. Marc Hogan of Pitchfork Media criticized the band for its songwriting, melodies and Christian symbolism, saying that "Robbers and Cowards insults our intelligence a few times too often." Cat Dirt Sez of the San Diego CityBeat said that Hogan's review was an example of lazy journalism, with lead guitarist Jonnie Russell saying that the reviewer wanted a wittier approach to the album rather than a thoughtful assessment of it.