Amazon Thursday said it would give $20 gift cards and pay shipping costs for customers affected by problems at UPS and FedEx that delayed some Christmas package deliveries.

The Amazon pledge came after UPS in particular came under fire for late packages despite vows from retailers to meet a December 25 deadline.

Some customers took to Twitter to voice their displeasure, likening one or both delivery giants to the "Grinch who stole Christmas."

Amazon pointed the finger squarely at the delivery companies. The online retail giant did not give estimates for the number of affected shoppers.

"Amazon fulfillment centers processed and tendered customer orders to delivery carriers on time for holiday delivery," said Amazon spokeswoman Mary Osako. "We are reviewing the performance of the delivery carriers."

Walmart also will provide gift cards to customers who did not receive packages by the promised deadline, the New York Times reported.

Walmart did not immediately respond to requests for comment.

UPS spokeswoman Natalie Black said the problems stemmed from a "perfect storm" caused by an unexpected jump in Christmas shopping the last two weeks, a compressed holiday shopping season in 2013 due to the late date of Thanksgiving and some severe weather that halted some deliveries.

"The result is that some packages that were set to be delivered on Christmas Eve were delayed," Black said.

A FedEx spokesperson also reported a "surge" in volume, but said the rise was typical.

"We had minimal service disruptions despite the increase in volumes, and are working directly with customers who may have experienced any delays," said the FedEx spokesperson.

Investors shrugged off the news. UPS gained 0.2 percent, while FedEx rose 0.9 percent.

The delivery woes suggested the retail sector is still adjusting to shifting customer behavior with the rise of online shopping.

More retailers have promised to execute Christmas-deadline deliveries ordered later and later in the season.

"There will be a few glitches in the next few years," predicted Chris Christopher, director for consumer economics at IHS Global Insight. "Whenever you're growing at double digits like this, there's bound to be this kind of thing happening."

Christopher expects online sales gains of 13.5 percent for the 2013 holiday season, compared with an increase of just 3.2 percent for the overall retail market.

Given its rising importance, retailers will likely increase delivery capacity next Christmas after this year's problems, Christopher said. Consumers are also likely to take additional steps, such as ordering earlier in the season, he said.

Early data on the overall season pointed to mixed results.

An analysis by MasterCard Advisors showed US holiday retail sales improved 2.3 percent, with strong gains in jewelry and modest growth in apparel.

Online retail sales from desktop computers rose 10 percent from a year ago to $42.8 billion, said comScore. However, the report showed "considerably softer" sales than expected in the final week before Christmas.

Christopher of IHS said the sales growth was on track to be the worst since 2009, despite the strong gains in the online market.

Analysts say the retail sector typically produces individual winners and losers depending on whether a particular company falls in or out of fashion.

That said, the 2013 holiday shopping season is regarded as one of the most heavily promotional in recent years, with retailers like Walmart and Best Buy pricing aggressively.

Amazon characterized its overall holiday shopping season as the "best ever" in the company's history.

Particularly popular was the "Amazon Prime" service, which provides free two-day shipping services and streaming of some television shows and movies for $79 a year.

Amazon said it signed up more than one million customers for its "Prime" service in the third week of December.