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.

Kanhaiya Kumar was arrested last month, after a rally against the execution of a Kashmiri separatist convicted over the 2001 Indian parliament attack.
A panel from Jawaharlal Nehru University (JNU) probing the incident reportedly recommended the expulsion of five students, including Mr Kumar.
Mr Kumar was released from jail after being granted bail earlier this month.
His views have been divisive in India with some calling him "anti-national".
Kanhaiya Kumar: India's most loved and loathed student
The Press Trust of India news agency reported that the university panel had found the students guilty of "violating university rules and discipline norms".
Apart from Mr Kumar, the panel has also reportedly recommended the expulsion of Umar Khalid and Anirban Bhattacharya, two other students who remain in custody.
Reports say a final decision on the panel's recommendation will be taken by the vice chancellor of the university.
Authorities allege Mr Kumar and others shouted anti-India slogans at the 9 February rally on the campus.
Critics have condemned the charges against the students as an assault on freedom of expression, but government ministers have refused to back down, vowing to punish what they describe as "anti-national elements".
The rally that prompted the arrests was to mark the third anniversary of the 2013 hanging of Mohammed Afzal Guru.
Guru was one of those convicted of plotting the 2001 parliament attack - charges he always denied. The attack, which left 14 people dead, was blamed on Pakistan-based militants fighting Indian rule in Kashmir.
Indian opposition parties see the affair as an attempt by the BJP to push its Hindu nationalist agenda, correspondents say.
There have also been counter protests by those who say JNU is a hotbed of "traitors" and should be "cleaned up".
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.
[NEXT_CONCEPT]
A student leader from a top university in India charged with sedition may be expelled from campus, reports say.