Music stars including Sir Elton John and Radiohead are putting pressure on the government to resolve the problems around post-Brexit EU touring.
UK artists will face red tape and fees for visas to play in some EU countries.
Sir Elton John told The Guardian: "Either the Brexit negotiators didn't care about musicians, or didn't think about them, or weren't... prepared."
But Culture Minister Caroline Dinenage said the government had "pushed" for a solution and the door was still "open".
She told MPs on Monday that the government had put forward a "very straightforward" plan to allow musicians to travel without work permits, drafted "in consultation with experts from the UK to creative sectors". She added: "Quite simply the EU rejected this proposal."
Brussels has previously argued the opposite, saying it was in fact the UK that turned down its offer.
Ms Dinenage said the EU proposal was part of a wider package that was "not consistent with the manifesto commitment to take back control of our borders" and not "consistent with the idea of Brexit that the majority of people in this country voted for".
Her comments came after Sir Elton said the UK's Brexit negotiators had "screwed up", and that "it's ultimately down to the British government to sort it out: they need to go back and renegotiate".
Meanwhile, Radiohead's Colin Greenwood said the government "didn't do enough" for the creative industries in negotiations.
"Like Hamburg to the Beatles, Europe was crucial to our growth as a band," the bassist wrote in The Guardian.
"It allowed us to see ourselves untethered from our UK roots and to imagine a life in music that could reach audiences everywhere. We made enduring friendships, toured with musicians from Europe, and dived deep into its clubs, festivals, record stores and music labels."
"What will playing in Europe be like now, after Brexit?" he asked, pointing to the additional costs of carnets (a customs document) on equipment.
"I spoke to several old friends who've had years of experience planning Radiohead tours. Adrian, our touring accountant, said it will be more clunky and expensive."
Greenwood concluded that the "diminishment" of UK music "would deprive us all", and it was therefore time for the government "to admit it didn't do enough for the creative industries during the Brexit negotiations and look to renegotiate on the provision for touring in Europe".
Irish singer Ronan Keating echoed those sentiments, arguing that post-Brexit red tape would be "devastating" for the live music industry, and in particular for newer acts.
"We're talking about grassroots, upcoming artists," the former Boyzone star told BBC Breakfast on Monday. "It's not so much about larger artists who already have back catalogues and careers.
"There's no money in record sales, the way that they [artists] make money is actually touring.
“We won’t be able to go touring, it’s just not going to happen”— BBC Breakfast (@BBCBreakfast) February 8, 2021
Singer-songwriter Ronan Keating tells #BBCBreakfast the post-Brexit conditions for touring musicians will be devastating to the live industry. https://t.co/4GLT4Zi6Lr pic.twitter.com/AiFOyfSxWJ
"So, to slap this on them, it's just going to be devastating for the live industry. We won't be able to go touring."
Speaking in the House of Commons last week, Culture Secretary Oliver Dowden admitted the barriers facing British musicians who want to tour in the EU were "absurd and self-defeating".
He said the situation "could have been solved" before 1 January, and laid the blame with the EU.
The EU's Brexit negotiator Michel Barnier said last month that the result was regrettable but one of the "inevitable consequences" of Brexit.
Also last month, Sir Elton, Liam Gallagher and Nicola Benedetti were among 110 artists to sign an open letter to the government, which declared performers had been "shamefully failed" by new visa rules.
Sir Elton then told the BBC he had held "very positive" talks with Mr Dowden last week about what could be done, despite the matter having been previously "swept under the carpet".
Monday's Parliament hearing came as a result of a petition by live music camera director Tim Brennan, which has reached more than 280,000 signatures. The threshold for a debate to be considered by Parliament is 100,000.
Ahead of the debate, Brennan shared a blog post online by experienced artist, composer and sound designer, Robin Rimbaud, who said he and other professionals had been left in "a compromising and harrowing situation".