The mad dash for shift dresses and floral hammocks in the Lilly Pulitzer for Target collection turned into a whirlwind that nearly crashed the Minneapolis-based retailer’s website early Sunday morning. The collection sold out in many stores within minutes.

Some dejected customers who stayed up all night to buy pieces online and came away empty-handed quickly took to Twitter to call the situation an “epic fail” for Target. But others said it was proof of the intense interest Target can still generate through limited-time designer partnerships.

For its part, Target apologized to customers who were not able to access the collection online before most of the items had sold out.

“We never want our guests to be disappointed,” said Joshua Thomas, a Target spokesman. “We share their disappointment with the experience of shopping online. It doesn’t match what we aim to provide them, which is an easy, seamless, consistent experience.”

Target often teams with up-and-coming designers, so Lilly Pulitzer is one of the more iconic, mature brands it has partnered with. The preppy Palm Beach-inspired brand has a devoted following, especially on the East Coast and in the South, that gravitates to its vibrant ­colors and floral patterns.

In the weeks leading to Sunday’s launch, the collection received a huge amount of buzz on social media. But no one knew exactly how big it would be until Sunday.

While many angry shoppers claimed that Target’s website crashed, Thomas said that was not the case. Rather, he said the overwhelming online traffic led the retailer to take steps to manage the situation that slowed the site down. At certain times, Target only allowed some customers to access parts of its website. And at one point, Target made the site inaccessible for about 15 minutes in order to grapple with the traffic and avoid a full-blown crash.

Target never gives an exact time in advance of when its designer partnership collections will be available online since it’s usually a rolling launch as the website updates throughout the early morning hours. While Target had hoped to make the Lilly Pulitzer collection available online by about 3 a.m., it was delayed until 5 a.m. because of high traffic, Thomas said.

“There was extreme interest, extreme demand — traffic that would be on par with Black Friday,” he said.

While many customers came away with a sour taste in their mouth, some retail experts said it shouldn’t leave a lasting bruise on Target’s reputation. After all, these events are designed to build hype.

“Customers have to realize that products are going to be in short supply,” said Dave Brennan, co-director of the University of St. Thomas Institute for Retailing Excellence.

That’s one of the reasons why designers agree to do them in the first place, so they don’t have to worry about damaging their full-price line while still gaining exposure, he said.

“It works very well for Target and it works very well for the designers,” he said. “But maybe not so well for the consumer because there’s not enough merchandise to meet their needs.”

The shopping frenzy was reminiscent of another much-hyped Target collaboration with the Italian design house Missoni in 2011 in which stores were quickly cleared out of the merchandise. In that case, Target’s website did actually crash, highlighting weakness with its online operations.

In the last year or so, Target has rebuilt about two-thirds of from the bottom up to make it faster and enhance its functionality. But Sunday morning’s snafus showed the retailer still has some work to do to shore up its site.

Target is not the only retailer to have struggled recently during a major event as consumers become more accustomed to shopping online. Richfield-based Best Buy took its website offline a couple of times last year on Black Friday to cope with a surge in mobile traffic.

On Sunday morning, Lilly Pulitzer fans waited, sometimes for hours, for stores around the country to open.

At the downtown Minneapolis store next to Target’s corporate headquarters on Nicollet Mall, the line of a few hundred people snaked around the building. The women’s dresses and home goods were snatched up within minutes. By midafternoon employees were replacing some of the Lilly Pulitzer displays with other products. But a handful of Lilly Pulitzer items remained, including some floral-printed nail files and a handful of girls’ dresses.

Gwenia Fiskevold Gould, 26, tried to buy a couple pieces online the night before, but quickly gave up after 20 minutes of trying. She had better success at the St. Paul Midway store, which she got to around 7:30 a.m., a half-hour before it opened.

“Some of the girls in line had stayed up all night,” she said. “One of the girls in front of me said she had bought a bunch of stuff online, but she wanted to go to the store, too.”

While employees instructed shoppers to walk once the doors opened, some couldn’t help but run. Some people filled heaping shopping carts, Gould said. Most of the merchandise was snatched up in 10 minutes or so, but she managed to get her hands on some wine charms and a couple of tops.

Within hours of the launch, many of the items also began showing up on eBay. By Sunday afternoon, more than 16,000 items appeared at marked-up prices when searching that site for “Lilly Pulitzer for Target.”

Target doesn’t have any plans to replenish the ­products in stores.

“Next time either 1) don’t promote something that most people will never see or 2) significantly increase production #whatafiasco,” one frustrated shopper tweeted at Target on Sunday morning.

Thomas countered that it’s hard to anticipate how strong the demand is going to be for any collection.

“We never intend for a collaboration to be in store for one day,” he said. “We anticipate they will be in store for a couple of weeks … You just don’t know how the consumer is going to react until you put it in front of them.”

In any case, one thing is now clear, Thomas added.

“At this point, Lilly Pulitzer is the most talked about designer collection in our ­history.”