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."
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.