The ex-chancellor said he respected the decision to prioritise immigration controls and withdrawal from the European Court of Justice instead.
He was speaking as MPs began a second day of debating the draft legislation that will allow formal talks to begin.
Downing Street said: “The former chancellor speaks for himself.”
The government is expected to win the vote later, with most Tory and Labour MPs set to back its bill.
If the bill is passed, Article 50 of the Lisbon Treaty, triggering formal Brexit talks, can be invoked.
Mr Osborne said the Government had chosen “not to make the economy the priority in this negotiation, they have prioritised immigration control”, while the EU’s priority will be to “maintain the integrity of the remaining 27 members of the European Union”.
He predicted the talks with the EU would be bitter, and a trade-off between “access and money”.
Mr Osborne said he had “passionately” campaigned for a Remain vote in the EU referendum and had sacrificed his position in government for the cause.
But he said for Parliament not to allow Article 50 of the Lisbon Treaty to be invoked would “alienate people who already feel alienated” and could cause a “deep constitutional crisis”.
Media captionDavid Davis: Listen to the people on Brexit
Earlier MPs were told that European Commission chiefs plan to ask the UK to pay up to 60bn euros for its separation from the EU.
Sir Ivan Rogers, the UK’s former ambassador to the EU, told a Commons committee the commission’s chief negotiator Michel Barnier and other key figures were “openly” saying the UK’s total financial liabilities would be in the order of 40 to 60bn euros.
He said the “unreasonable” figure represented a “predictably hard line”.
In other Brexit news, Prime Minister Theresa May confirmed a White Paper setting out her Brexit strategy would be published on Thursday.
The official document, which will include a desire to secure the status of EU nationals in the UK and Britons abroad, is separate to the Brexit bill being debated by MPs.
The vote on the bill is expected at about 19:00 GMT.
Labour leader Jeremy Corbyn faces a rebellion by a number of his MPs, including several frontbenchers, while the SNP and Liberal Democrats are also promising to oppose ministers.
Mr Corbyn has imposed a three-line whip – the strongest possible sanction – on his MPs to back the bill, which is only two lines long.
Media captionStarmer: Brexit bill difficult for Labour
If the vote goes the government’s way, the bill will return to the Commons next week for the committee stage, when opposition parties will try to push through a series of amendments.
The bill was published last week, after the Supreme Court decided MPs and peers must have a say before Article 50 could be triggered.
It rejected the government’s argument that Mrs May had sufficient powers to trigger Brexit without consulting Parliament.