Williams say it was "embarrassing" to miss two days of pre-season testing because their car was not ready.
The Williams, driven by Briton George Russell, finally made it on to the track at the Circuit de Barcelona-Catalunya on Wednesday - with a day and a half left of the four-day test.
Deputy team principal Claire Williams said: "It's not a situation that we anticipated, or that we ever wanted to find ourselves in."
Debutant Russell was 13th fastest.
The 21-year-old was eight seconds off the pace set by Toro Rosso's Daniil Kvyat, who - after a late run on the fastest tyre - pipped Alfa Romeo's Kimi Raikkonen by 0.058 seconds.
Williams added: "We're not just disappointed. It's embarrassing not bringing a race car to a circuit when everyone else has managed to do that, particularly a team like ours that has managed to bring a race car to testing for the past 40-odd years."
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Williams said she wanted to apologise to the team's fans, but also to drivers Russell and Robert Kubica, who is returning to F1 after an eight-year absence following a 2011 rally crash that left him with partial movement in his right arm.
Williams said the delays "became apparent quite late on", and after initially hoping they could make the second day of the test "parts just weren't coming through as we hoped they would".
She refused to expand on why the problem happened.
The situation has raised questions within the team about the future of chief technical officer Paddy Lowe, who is ultimately responsible for all technical parts of the company.
The team cancelled a media briefing that had been scheduled for Lowe, saying it would now not take place until next week's second test after the car had undertaken significant running.
And Williams ducked questions about Lowe, saying: "I've read a lot of speculation about his position. Right now all I am focused on - and the team should be focused on - is making sure the car is in the right place."
Kubica is due to drive the car on Friday morning, before Russell runs again in the afternoon, and Williams is hopeful the team will be able to make up for lost time.
"We've missed two days of testing, and that's not ideal," she said. "That's a lot of potential kilometres. But I don't think that we will actually know the full impact of having missed those days until probably a bit later on.
"Clearly we're doing everything we can to condense the programme that we had, to make sure that we maximised the time available and we really focused our efforts and attention on the most important and critical areas to make sure the car is in the best shape possible for Australia."
Russell managed 23 laps, with a best time of one minute 25.625 seconds.
Williams said the team were still waiting for parts to arrive to allow them to concentrate on an aerodynamic assessment programme on Friday.
Ferrari continue to impress
Kvyat's late dash on the softest tyres displaced Raikkonen, who had topped the times for much of the day.
Renault's Daniel Ricciardo also leapt up the times late in the day, with a run on the second-softest tyre, to push Ferrari's Sebastian Vettel down to fourth.
Nevertheless, Ferrari continued to impress with their pace and reliability - Vettel and new team-mate Charles Leclerc were fastest on the first two days.
World champion Lewis Hamilton, who was 12th fastest for Mercedes, said Ferrari were "very strong", adding: "It appears they have a better package than last year, which means it will be a bigger challenge for us."
Hamilton added Mercedes were concentrating on learning about their car and it would not be until the second pre-season test next week that people would have a better idea where the teams stood.
Fastest times, day three, first pre-season test at the Circuit de Barcelona-Catalunya
1 Daniil Kvyat (Rus) Toro Rosso 1:17.704 *****
2 Kimi Raikkonen (Fin) Alfa Romeo one minute 17.762 seconds *****
3 Daniel Ricciardo (Aus) Renault 1:18.164 ****
4 Sebastian Vettel (Ger) Ferrari1:18.350 ***
5 Max Verstappen (Ned) Red Bull 1:18.787 ***
6 Nico Hulkenberg (Ger) Renault 1:18.800 ****
7 Romain Grosjean (Fra) Haas 1:19.189 ***
8 Pietro Fittipaldi (Brz) Haas 1:19.249 ****
9 Carlos Sainz (Spa) McLaren 1:19.354 ***
10 Sergio Perez (Mex) Racing Point 1:20.102 ***
11 Valtteri Bottas (Fin) Mercedes 1:20.693 ***
12 Lewis Hamilton (GB) Mercedes 1:20.818 ***
13 George Russell (GB) Williams 1:25.625 ***
Key: * = C1 tyre (hardest); ** = C2 (second hardest); *** = C3 (middle); C4 **** = (second softest); ***** = C5 (softest)