Whitehall civil servants display a "poor knowledge and understanding" of devolution, says a report by the Welsh Affairs Select Committee.
More training is needed for Whitehall to understand devolution, while their colleagues in Cardiff need to show more confidence, the report says.
The select committee said reform of the way Wales is funded was needed and that a new funding formula must be "fairer".
Welsh Secretary Peter Hain said the report "makes very interesting points".
The report says Westminster and Welsh governments need a better relationship.
It follows a series of hearings by the committee, taking evidence from civil servants and politicians.
The MPs said they were concerned about delays to Welsh law-making which may have been caused by the time taken to clear legislative competence orders (LCOs) through Whitehall.
Until an LCO is passed, the Welsh assembly cannot take control of law-making in the devolved policy area covered by the order.
The report says: "They (LCOs) are frequently not given priority within Whitehall departments, which may affect the delivery of the Welsh assembly government's legislative timetable."
It adds that Whitehall had not fully engaged with devolution and recommended more training for civil servants.
The MPs also said the means by which Wales was funded, the Barnett formula, "does not seem to us to be guaranteed to be sustainable" and should be replaced.
The report states: "We urge the government, as a priority, to review the current arrangements and to adopt a needs-based approach to a new financial settlement...bringing about a formula which is fairer to Wales."
The committee recommends the Cabinet Office, "with its position close to the Prime Minister" should take on this central responsibility.
The MPs found that the memorandum of understanding which forms the basis of inter-governmental relations between Wales and Whitehall needs a "broad review" and that relying on informal links is not good enough.
It says Whitehall responsibility for devolution strategy lacks a "strong centre" as it is shared between the Ministry of Justice, the Cabinet Office and the Wales Office.
Committee chair Hywel Francis said the arrival of democratic devolution for Wales over the past decade had been the biggest constitutional change for Wales since 1536.
He said: "Our inquiry must be seen in this historical context.
"Ministers and senior civil servants at both ends of the M4 need to be more coordinated, strategic and transparent in their development and delivery of devolution with a much higher priority given to awareness raising of Welsh devolution in Whitehall.
"Welsh ministers and Welsh civil servants of both governments should be much more pro-active in achieving this."
Lord Dafydd Elis-Thomas, presiding officer for the National Assembly for Wales, said the report had correctly identified a lack of transparency between the assembly and Whitehall.
He told BBC Radio Wales: "The difficulty has been, and is endemic in the history of the UK, that people in Westminster do not realise that the UK is a federal state, where powers are distributed differently.
"Of course there is need of a cultural change - that's not just in Whitehall, that's also in Wales, that's also in our relationship with the EU."
He said the "Whitehall machine needs to be far more involved in devolution so they understand what inter-governmental relations really are about".
Welsh Secretary Peter Hain said the report "makes very interesting points" which would repay the careful consideration he intended to give it.
He said: "I am pleased they agree with me that there must be a strong voice for Wales, in the form of a secretary of state for Wales sitting at the cabinet table."