Back in March, the San Francisco food delivery startup Eat24 staged a "breakup" with Facebook.

The company had poured $1 million into Facebook advertising in 2013 alone and picked up more than 70,000 fans, but it wasn't clear the investment was really getting anything.

A month later, the company reported on the impact of the separation - leaving Facebook, it turned out, had no discernible consequence. In fact, the number of people actually opening the company's marketing e-mails picked up.

A new survey from Gallup confirms what Eat24 learned by trial: Social media just doesn't hold much sway over consumer decision making.

Companies spend millions annually on social media networks such as Facebook and Twitter, buying up promoted posts and running promotions meant to rack up fans. Most hire social media marketers and strategists, tasked with growing followers and consumer engagement. U.S. companies spent $5.1 billion on social media advertising in 2013.

Those efforts, though, may be in vain.

"Social media are not the powerful and persuasive marketing force many companies hoped they would be," concludes Gallup, which released the research Monday as part of its State of the American Consumer report.

Of the more than 18,000 American consumers polled, 62 percent said social media had no influence on their buying decisions. Just 5 percent said it had a significant influence.

Moreover, it seems consumers scrolling through their Facebook feeds looking for photos of friends' babies are turned off by finding instead a hard sell.

"They are far less interested in learning about companies and/or their products, which implies that many companies have social media strategies in place that may be largely misdirected," the report found.

Already some brands are shifting gears, viewing places like Facebook and Twitter as a medium for conversation with customers who are already fans, rather than a place to push brand awareness.

Recently, changes to the algorithm that manages a Facebook user's news feed decreased the reach of brands. Content is now organized according to what Facebook thinks a user wants to see rather than chronologically - and often that's not a post by a brand a user has "liked."

A March analysis by the marketing firm Ogilvy & Mather estimated so-called organic reach - or how many eyeballs a piece of unpaid brand content sees -plummeted to about 6 percent, dropping nearly in half from peak levels months earlier. That change was part of what prompted Eat24's departure from the network.

Ogilvy's report concluded that "the model has shifted" and suggested in the future brands will thrive on Facebook only by supplying their fans with share-worthy content "they will really love."

Gallup's findings similarly suggest that brands have just been using social media poorly. The survey found consumers are more likely to engage with companies that seem more genuine and responsive.

The social network Pinterest seems, at least early on, to be a more natural fit for brands. Pinterest is akin to a digital bulletin board where users pin images and links, frequently for items they would like to purchase. So on Pinterest, a suggestion, for example, from Banana Republic for a summery blouse doesn't seem out of place.

Brands, Gallup's survey suggests, will never win with content consumers aren't interested.

In a snarky response to Eat24's breakup letter, Facebook director of global communications Brandon McCormick spelled it out, defending Facebook's new News Feed organization.

"There is some serious stuff happening in the world and one of my best friends just had a baby and another one just took the best photo of his homemade cupcakes," he wrote. "What we have come to realize is people care about those things more than sushi porn."

Kristen V. Brown is a San Francisco Chronicle staff writer. E-mail: Twitter: @kristenvbrown