Brian Fallon of The Gaslight Anthem performs at the Independent in San Francisco on July 5, 2012. Roman Gokhman/STAFF.

SAN FRANCISCO — Brian Fallon, frontman of The Gaslight Anthem, made a point of self-deprecatingly mocking his lack of education, the New Jersey punk-rock band’s appearances and their home state Thursday night at Gaslight’s sold-out show at the Independent.

“Sorry we’re not better-looking,” he said, following blistering concert opener “Drive,” off of the band’s 2007 debut, Sink or Swim. “I don’t know what a pronoun is; I’ve never been to college,” he added later.

To the contrary, Fallon came off as very articulate and had a great sense of humor, which blended well with the rough-around-the-edges, bare-knuckle performance the Gaslight Anthem put on as the band prepares for the release its new album, Handwritten, later this month.

Fallon riffed with the crowd about Scientology (although he needed a bit of explanation that those folks are down in Los Angeles and not in the Bay Area). He went through a couple of North Jersey stereotypes and asked who in the crowd was from back-home. When an overly-enthusiastic fan responded, Fallon remarked, “You know we have, like, eight songs about leaving, right?”

And toward the end of the show, he conversed with a club waitress across the room, offering to pay $40 if she delivered two Cokes to the stage. When she did a few songs later, he paid with guitarist Alex Rosamilia’s cash, prompting a five-minute conversation with Rosamilia about how the waitress thanked the singer but not the guitarist. Maybe she should send Rosamilia a thank-you card, Fallon suggested, jokingly. Because $40 is a pretty big tip for two soft drinks, after all.

The band’s performance itself was as strong as Fallon’s improv routine, with punk songs one right after the other, such as “Old White Lincoln,” “Casanova, Baby!” and “Angry Jonny and the Radio.”

A fewer slower tunes made it into the middle of the setlist, but they were no less intense. “Blue Jeans and White T-Shirts,” off 2008’s Senor and the Queen EP, was a sing-along favorite. Gaslight also played three songs off Handwritten: Lead single “45,” as well as “Biloxi Parish” and “Here Comes My Man.” All three fit in seamlessly with the band’s older material.

The only real downside to the show was a lack of songs from Gaslight’s 2010 record, American Slang. While the album helped propel the band into the mainstream, it was a commercial disappointment for the band and Fallon has said in recent interviews that he and his bandmates could have improved it. I disagree and would have appreciated hearing more than the title track and “The Queen of Lower Chelsea,” which were hidden in the middle of the set.

Follow editor Roman Gokhman at Twitter.com/RomiTheWriter.