By Rolfe Winkler and Alistair Barr 

Fast-rising expenses eroded Google Inc.'s first-quarter profits, disappointing investors and sending Google shares lower in after-hours trading.

The Internet-search giant said revenue for the quarter rose 19% to $15.4 billion from $13 billion a year earlier, excluding the Motorola Mobility business Google plans to sell to China's Lenovo Group Ltd. Analysts had projected revenue of $15.5 billion on that basis, according to S&P Capital IQ.

But expenses grew faster--at 23%. As a result, Google's net income increased 3% to $3.65 billion, or $5.33 a share, from $3.53 billion, or $5.24 a share. The figures were adjusted for the pending Motorola sale and a 2-for-1 stock split.

Excluding stock-based compensation and other items, Google said earnings were $6.27 a share; on that basis, analysts had predicted $6.41 a share.

"The top line was pretty good, but the margin compression probably disappointed the market," said Brian Wieser, an analyst at Pivotal Research Group. "The margin erosion trend seems to be well in place."

Shares fell nearly 3% in after-hours trading Wednesday, after rising by a similar amount to $563.90 during the regular trading day. Since hitting a peak in late February, Google shares have followed the broader stock market downward. Still, shares have risen about 60% since the beginning of 2013.

Mr. Weiser said Google's profit margins have declined as the company expands into more businesses. Newer businesses like online-video service YouTube, as well as display advertising, are less profitable than the company's original search-advertising business, Mr. Wieser said.

Chief Financial Officer Patrick Pichette told investors on a conference call that operating expenses rose in part because of one-time research-and-development costs related to Google's $3.2 billion purchase of home-automation company Nest Labs. Research-and-development expense increased 31% from a year earlier to $2.1 billion.

"There will always be one-time items for a company like Google that does so many acquisitions," said RBC Capital Markets analyst Mark Mahaney, who added that Google is smart to continue making acquisitions to find new growth opportunities.

Wall Street estimates suggest that Google's profit margins will remain roughly flat in the future as revenue continues to grow strongly, but Mr. Wieser said that isn't realistic. He pointed to some of Google's more-ambitious new projects, such as self-driving cars and a high-altitude Internet service, which may also be less profitable than the search business.

Google also is increasing investments in data centers and other infrastructure to beef up its computing capacity, something Google's Mr. Pichette called strategically important. Capital spending nearly doubled from a year earlier, to $2.3 billion from $1.2 billion.

As a result, Google generated less cash--after subtracting capital expenses--than in any quarter in at least two years.

"[Capital expenditure] was quite a bit higher than Street estimates, but keep in mind they are building out a lot of infrastructure, which in our view is certainly justified by the massive revenue opportunities still ahead for Google," said Colin Sebastian, an analyst at RW Baird.

Google said revenue in its core advertising business rose 17%. Clicks on advertiser links next to Google's search results increased 26% from a year earlier.

But the amount Google got paid per click fell 9% from a year earlier, continuing a trend, as a higher percentage of searches occur on smartphones, where Google's clicks are less valuable. The smaller screens and limited bandwidth of smartphones make them a less-appealing tool than desktop computers for consumers looking to buy products or services online.

Marketers that work with digital-ad firm Rimm Kaufman Group paid about 60% less for smartphone clicks than desktop clicks in the first quarter to generate an equivalent payback.

Google's earnings report came a day after Yahoo Inc. said its revenue, after commissions paid to partners, grew for the first time in more than a year. Yahoo reported that its revenue, minus commissions paid to partners for Web traffic, rose 1% in the latest quarter.

While Yahoo struggles to regain its footing in online advertising, Facebook Inc. has emerged as Google's chief rival. Research firm eMarketer predicts that Facebook's net advertising revenue will grow 54% to $10.8 billion this year while Google's will grow 14% to $43.5 billion.

To build upon its dominant position, Google is trying to prove that its ads work. The company now provides advertisers with data showing the sales the advertiser is generating via desktop computers but which Google says can be traced back to clicks on smartphone ads.

The idea is to persuade advertisers to bid more for smartphone clicks says Mark Ballard, research director at Rimm Kaufman Group.

Meanwhile, it also has a pilot program under way to match the anonymous tracking "cookies" on users' computers to in-store sales information collected by data providers like Acxiom Corp. and DataLogix Holdings Inc. The idea is to connect online ads to offline purchases, and therefore to convince advertisers to spend more with Google.

Write to Rolfe Winkler at rolfe.winkler@wsj.com and John Kell at john.kell@wsj.com

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