The online greeting card and gift firm was bombarded with complaints about gifts that were damaged, late or failed to arrive.
Among the complaints posted on social media were photos of flowers with wilted leaves and snapped stems and a smashed vase.
One customer claimed their mother took delivery of a flower box to find it was empty.
The company spent Mother's Day answering the stream of complaints on Twitter and Facebook before reportedly attributing the problems to "an issue" with a supplier.
Michael Blair wrote to Moonpig on Twitter: "OMG ! Flowers just arrived for Mum - broken, ripped, dead, disgusting! And no card til Monday either!"
Becky Peters, from Newport, South Wales, tweeted: "@MoonpigUK two years in a row you have disappointed me, you've lost a customer. Don't advertise your cards to be delivered on Mother's Day if they're not going to arrive."
Helen Palmer tweeted a photo of a sorry-looking bouquet and a damaged vase along with the comment "#unhappy Mother's Day".
Jakeyjelly tweeted: "@MoonpigUK ordered my Mother's Day flowers and got the card but no flowers in sight absolute disgrace!" alongside a photo of an empty box.
In adverts ahead of Mother's Day the firm said it would take orders for gifts until 2pm on Friday and flower orders up to 4pm on Saturday.
Flowers and plants were supposed to arrive between 8am and 9pm over the Mother's Day weekend, the company said.
A spokesman for Moonpig told the BBC: "We can confirm that an issue with one of our suppliers has delayed the delivery of flowers to some of our customers this weekend.
"We know how important Mother's Day is and we have apologised to and compensated all customers who have experienced a delay.
"We've been working hard to put things right and by the end of Mother's Day almost all orders have been delivered. We hope our customers accept our sincere apologies."
Other customers were more positive about their service from Moonpig, whose personalised greeting card service accounts for a major share of the UK online market.
Melissa Rose Ledbury wrote on Facebook: "Quite surprised to see all the negative comments, I was going to say I'm really pleased with my order, my mum text me around 10 to say her flowers had arrived and said they look lovely!"