The question we’re left with after watching “Paul” is this: How could Simon Pegg, one of the guys behind the astute satires “Shaun of the Dead” and “Hot Fuzz,” be responsible for something this lazy? With so much comedy potential in the premise of science-fiction nerds encountering an actual space alien, how did “Paul” turn out to be a setback in the search for signs of intelligent life?

Perhaps there were unforeseen compatibility issues. Pegg wrote the screenplay with Nick Frost, the portly fellow who co-starred with him in the just-mentioned films. But this is Frost’s first major writing credit — in the past, Pegg’s writing partner has been Edgar Wright, who has also been the duo’s director. “Paul” is directed by Greg Mottola, who made “Superbad” and “Adventureland.” As talented as Pegg, Frost, and Mottola are at various things, their collaboration on this particular project is disappointing. I get that a raunchy comedy about aliens is bound to include a couple jokes about anal probes, but “Paul” has about a hundred. “Paul” is obsessed with anal probes. Eight years from concept to finished product and that’s the best they can come up with?

Pegg and Frost are Graeme and Clive, Brit nerds who have made a pilgrimage to San Diego Comic-Con, i.e., geek Mecca. (This is where a fantasy author who goes by the name Adam Shadowchild can be called “the coolest guy in the world” without irony.) After the convention, Graeme and Clive drive an RV — which they rented? I guess? — on a tour of famous UFO spots in the American Southwest.

It is during this trek that they meet Paul (voiced by Seth Rogen), an honest-to-goodness little green man. In fact, he is the prototype for the “little green men” cliche, his image having leaked to the public numerous times since he crash-landed and was captured by the U.S. government in 1947. Though he’s spent the last 60-plus years locked away in a top-secret government facility, Paul is remarkably laid-back and friendly, not to mention well-versed in American pop culture. He smokes weed, too, though that may be the result of a stipulation in Seth Rogen’s contract.

Paul needs to get back to his home planet now, and Graeme and Clive are enlisted to help him. They are soon joined by Ruth Buggs (Kristen Wiig), a one-eyed fundamentalist Christian who doesn’t believe in evolution, much less extra-terrestrials. (Both views are quickly reformed.) The group is pursued by a federal agent named Zoil (Jason Bateman), two underling agents (Bill Hader and Joe Lo Truglio), Ruth’s gun-toting father (John Carroll Lynch), and a couple of angry rednecks (David Koechner and Jesse Plemons) — although I think the rednecks aren’t pursuing them so much as they’re coincidentally showing up at the same places, across several states.

That last point is emblematic of the movie’s lackadaisical attitude toward story, which is all the more disappointing when you recall how intricately “Hot Fuzz” and “Shaun of the Dead” were plotted. “Paul” is just as affectionate a tribute to its genre as those movies were to theirs; it just doesn’t have the ingenuity. It’s filled with references, both overt and subtle, to the alien movies that Generation X grew up with — Sigourney Weaver makes the obligatory cameo — but the references are seldom clever. (One exception: the suggestion that Paul was a secret consultant on Hollywood movies like “E.T.”) A lot of movie geeks will see themselves in Graeme and Clive, and apparently that’s all the movie was hoping to achieve: recognition.

In the right hands, this kind of spoof/homage can be nearly as iconic as the films it pays tribute to. (Think “Galaxy Quest.”) Pegg and Frost are an amiable onscreen pair, Wiig is sweetly dorky, Rogen is characteristically jovial as the voice of Paul. The raw materials are in place, and the film has some laughs. But it also has a million jokes about anal probes, alien genitalia, and people thinking Clive and Graeme are gay. These guys can do better than this.

C (1 hr., 44 min.; R, abundant harsh profanity, a lot of vulgarity, some sci-fi violence.)