He said he did not believe "sufficient has been done in the first 10 years of devolution to really tackle that and that's why the problems have now mounted up".
However, he also warned: "But that must not be at the cost of front line services or the assembly's capacity to create and support jobs in Wales at this critical time.
"We've already got unemployment including in south Wales constituencies like mine rocketing up and this is a time for the assembly government to be supported by Whitehall in making sure that as many jobs are supported as possible and that extra investment is provided to make sure that we can get spending back into the economy and make sure that we get out of this quickly."
Mr Hain also said he believed assembly finance minister Andrew Davies was beginning to tackle the issue.
"Both before devolution when I was a Welsh minister and observing it for the last 10 years or so that really there's not been a sufficient focus on efficiency savings within the Welsh administrative bureaucracy not with a purpose of cutting spending, but with a purpose of recycling that spending back into the front line," he said.
"Some if it has been done, not enough in my view. Andrew Davies as finance minister is making the first real attempt to do that, however in very difficult conditions because of the reduced spending capacity.
"If it had been done earlier on at a time of rising spending which the assembly has enjoyed all through its life until now then I think it would have been in a better position to move forward.
"But I want to see it come out of this with an increased capacity for frontline service investment, more jobs providing the services people need and not to have the efficiency cuts be at the expense of those frontline services," Mr Hain added.
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