Ministers said this risked "weakening" the UK's hand in negotiations.
The amendment, which was supported by 19 Tory rebels, means parliament could now force negotiators back to Brussels if they do not approve the terms put to them in October.
Baker added: "The EU (Withdrawal) Bill is about ensuring we leave the EU in a smooth and orderly manner, it is not a mechanism for overturning the referendum".
Both sides hope to negotiate the UK's withdrawal agreement by this October in order to give the United Kingdom and European Parliaments enough time to debate and vote on it before the moment of departure.
Dr Fox denied that a string of parliamentary defeats being inflicted on the Government would eventually force it into accepting that the United Kingdom would have to be part of some form of customs union with the EU.
The amendment, known as Clause 49, proposes that Parliament can determine the Government's course of action if the Commons rejects.
He said: "Parliament has voted to leave the European Union".
"We will now consider the implications of the House of Lords' decision".
The former Tory minister Viscount Hailsham said: "In democracies both Parliament and the electorate have the right to change their minds".
The cross-party amendment also calls on legislators to first seek approval from Parliament for the mandate of the second negotiating phase.
"I'm afraid it reveals the appalling lengths to which the die-hard Remainers are prepared to go to achieve their aims", he said.
Peers aim to give parliament the final say on what happens if there is no deal with the EU.
He also explained to BBC News that the amendment handed Parliament "unprecedented powers to direct the government in these negotiations... even keeping the United Kingdom in the European Union indefinitely".
"Firstly, the amendment tries to secure a vote for parliament before the negotiations have concluded".
Last week Brexit Secretary David Davis said the motion to be considered by MPs on the final deal would be amendable - raising the prospect of MPs having greater influence over the process.