Zynga Inc failed to boost the ranks of its online gamers in its first quarter as a public company, fanning worries that it will have to rely on new games and other ways to squeeze more revenue out of existing users.

The stock fell 81 cents, or 6 percent, to $13.98 after-hours. The price is up more than 25 percent since Facebook revealed on February 1 that 12 percent of its revenue comes from Zynga.

Zynga said Tuesday it had 54 million active daily users in the three months ended December 31, flat from the previous quarter.

They have to work harder to get existing traffic to pay more. That's a challenging proposition, said Sterne Agee analyst Arvind Bhatia.

Zynga's shares initially swung wildly after the results were released, as Wall Street puzzled over its better-than-expected revenue and slowing growth of bookings - or the money it makes upfront when people buy virtual items in its games - in the first half of 2012.

Zynga, which raised $1 billion in an initial public offering in mid-December, expects bookings of $1.35 billion to $1.45 billion this year.

We expect that growth will be weighted towards the back-half of the year with slower sequential growth in the first half of the year, the San Francisco-based company said in a statement.

Zynga estimated adjusted earnings of 24 to 26 cents a share in 2012, above analysts' average estimate of 22 cents.

Fourth quarter revenue rose 59 percent to $311.2 million. Analysts, on average, had expected $301.08 million, according to Thomson Reuters I/B/E/S.

Zynga had a net loss of $435 million, or $1.22 a share, compared with net income of $42 million, or 5 cents a share, a year ago.

Excluding $510 million in stock-based compensation, Zynga posted a profit of $37.2 million, or 5 cents a share, which beat analysts' average estimate of 3 cents.

Given Zynga's dependence on Facebook for most of its revenue, investors are closely watching its mobile strategy to make money from games on smartphones and tablets.

The company did not specify how much money it was making from mobile games, but Chief Executive Mark Pincus said on the conference call that Zynga was seeing its paying players grow very nicely for those games.

(Additional reporting by Gerry Shih in San Francisco; Editing by Matthew Lewis and Richard Chang)

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