The Commons Brexit committee's first report urges ministers to publish their Brexit plan by mid-February and give Parliament a vote on the final deal.
Jonathan Edwards, the committee's only Welsh member, accused Labour MPs of "gagging" Labour ministers in Cardiff.
The Welsh Government said it would work to ensure Brexit talks take account of "the interests of all parts of the UK".
As well as calling for clarity on the Brexit plan, the cross-party committee said the UK government should "strive" to ensure there was no return to tariffs or other trade barriers.
Chairman Hilary Benn said: "This is going to be a hugely complex task and the outcome will affect us all.
"The government needs to publish its Brexit plan by mid-February at the latest, including its position on membership of the Single Market and the Customs Union, so that it can be scrutinised by Parliament and the public."
He added that ministers should make it clear that Parliament would get a vote on the final deal.
Mr Edwards, MP for Carmarthen East and Dinefwr, welcomed the committee's support for continued free trade, but was unhappy it would not back his call for the devolved nations to be given a say on the final Brexit deal.
"By blocking my amendments to give Wales a voice, the Labour MPs on the committee have effectively gagged their Welsh Government colleagues," he said.
"That should ring major alarm bells for us in Wales. Westminster is intent on turning the UK into a unilateral state, dictating everything from Westminster, regardless of the needs and interests of Wales."
A Welsh Government spokesman welcomed the report's support for keeping trade open, and said it was involved in "ongoing discussions" with the UK government and other devolved administrations on the approach to Brexit.
"This is important work to ensure that the overall UK negotiating position takes into account the interests of all parts of the UK," the spokesman said.
"We look forward to continuing this constructive relationship after Article 50 has been triggered."
A UK government spokesman said it welcomed the report, but stressed: "We will set out our plans, subject to not undermining the UK negotiating position, by the end of March and that parliament will be appropriately engaged throughout the process of exit, abiding by all constitutional and legal obligations that apply."
Welsh Conservatives leader Andrew RT Davies said: "The committee recognises the damage that would be done if the Prime Minister were to be forced to disclose the government's negotiating position, and that is to be welcomed in what is by and large a sensible report."
A Plaid Cymru MP is "dismayed" fellow MPs will not insist on a Welsh say on the final terms of leaving the EU.