Ceding control of ARM is an example of the City mindset of "don't back [the] British economy", he told the BBC.
But Treasury advisor Eileen Burbidge said the sale was a "great deal".
On Tuesday, 95% of ARM shareholders voted to back the acquisition by Softbank.
Lord Myners said ARM, which provides chip designs used by firms including Apple, was a company "at the heart of the ecosystem of modern technologies".
He said control of ARM was now passing to a "very heavily-indebted, very unfocused business in Japan which does not have a good record of buying foreign companies and continuing to invest in them".
Decisions on the company's future would be made in Tokyo rather than Cambridge, he said.
Lord Myners added that commitments made by Softbank to the UK government to double the number of UK employees over the next five years and to keep the headquarters of the firm in Cambridge were "probably not legally enforceable".
"If ARM was an American company, a German, a French company or a Japanese company, it would not be able to be sold in 60 days - there would be a question of national significance and public policy to determine whether we should sell," he said.
However, Ms Burbidge said the £24.3bn deal was at a 43% premium above the closing share price the day before the deal was announced.
"It's obviously a very good deal for shareholders, [and] for a company that generated just shy of £1bn in turnover last year, it represents... a really great multiple and demonstrates that Softbank saw a lot of growth potential and opportunity in the company," she said.
She added that on the question of control, the company's designs were in 95% of the world's smartphones, so it was already making operational decisions based on a client base which was mainly outside the UK.
"It was being led by technology advances in [phone] handsets... by people outside of the UK, mostly from Asia, a lot from the North American companies, and so a lot of it was being defined by the market anyway."

Two sections of the A3055 Undercliff Drive suffered landslips in February 2014, creating a three-mile detour between Niton and St Lawrence.
Some residents, frustrated with delays, resurfaced the road themselves in October 2014, but the council shut it again for safety reasons.
The authority says the new route will only be open for local access.
The landslide, which happened during work to repair the road, caused eight homes to be evacuated.
The council said the collapse was caused by unusually heavy rain in an area of "known land instability" where there had been numerous landslips in the past.
The authority's planning committee has approved a new route, slightly inland, providing full access for local residents' vehicles, walkers, cyclists and horse riders, but closed to through traffic.
The work will be carried out by the authority's contractor Island Roads under an existing Private Finance Initiative (PFI) deal.
The company said the work would last eight weeks.
Resident Tim Wright said the solution was a "temporary scheme" which failed to address drainage problems.
The council said "retaining the existing drainage arrangements for the highway would not increase the potential for ground movement to occur".
Planning chairman Bob Blezzard said he hoped in the future there would be another application for the road to be "fully reinstated".
The £24.3bn deal to sell UK tech firm ARM to Japan's Softbank is an example of the UK "selling out of our winners", former City minister Lord Myners has said.
[NEXT_CONCEPT]
A main road on the Isle of Wight is to be repaired more than two years after it collapsed due to heavy rain.