It blamed its own "hubris" for overloading the Model X with technology.
It revealed that it delivered 14,820 cars in the first quarter, falling short of the expected 16,000.
It comes after the firm revealed that its new Model 3 car already has 276,000 pre-orders.
The carmaker said that it had delivered 12,420 Model S sedans and 2,400 Model X SUVs in the first quarter of 2016.
In a statement, Tesla added that its Q1 delivery count was "impacted by severe Model X supplier parts shortages in January and February that lasted much longer than initially expected".
It said that once "issues were resolved", production and delivery rates "improved dramatically".
"By the last full week of March, the build rate rose to 750 Model X vehicles per week, however many of these vehicles were built too late to be delivered to their owners before end of the quarter."
It was frank about the reasons for the delay: "The root causes of the parts shortages were: Tesla's hubris in adding far too much technology to the Model X in version one, insufficient supplier capability validation and Tesla not having broad enough capability to manufacture the parts in-house."
Back in February, Elon Musk admitted that the car had been "over-engineered".
The shortage involved about six out of the 8,000 parts that go into the Model X but Tesla did not specify which ones.
It has raised doubts about how prepared Tesla will be to deliver its new Model 3 car which was announced to much fanfare last week.
The basic model will sell for $35,000 (£24,423) - less than half the cost of Tesla's previous models - and has a range of at least 215 miles per charge.
The car is due to go on sale in late 2017 and customers must put down a $1,000 (£704) deposit. It can be ordered in advance to dozens of countries, including the UK, Brazil, India, China and New Zealand.
Mr Musk has revealed that the company is focusing on ramping up productions and will eventually need to build a factory in Europe to satisfy demand.
Stephanie Brinley, a senior analyst with research firm IHS, said that it was crucial that it gets production of the new vehicle right.
"Given its history of missed deadlines, this one needs to be met, to earn the faith of consumers and investors alike," she said.
Last year Tesla posted a net loss of $889m (£620m) for 2015, partly because of the large sum it spent on research and development.
Tesla Motors has revealed that supplies of its Model X electric car have been impacted by a shortage of parts meaning delays for some who have ordered them.