Chief of the Defence Staff, General Sir David Richards, said ministers had not taken into account reduced force sizes.
Sir David's comments came in an Oxford University lecture reported in the Daily Telegraph. In a statement through the MoD, he said "candid military analysis" made ministers aware of the limitations.
Sir David is said to have told Oxford's department of politics and international relations: "We have a whole load of tasks expected of us. Our political masters are quite happy to reduce the size of the armed forces but their appetite to exercise influence on the world stage is, quite understandably, the same as it has always been. Often politicians say to me 'can you go and do this?'. I say to them 'with what?'." He added: "If you reduce your armed forces, there is going to be a give - something gives."
His comments came against the background of the government's 2010 strategic defence and security review (SDSR) which introduced an 8% cut in defence funding and reductions of 30,000 personnel.
Sir David said one of his "biggest concerns" was about the number of frigates and destroyers in the Royal Navy fleet. He also expressed concern at what he considered missed chances to find a political way forward in Afghanistan.
"All the military can do is buy space and time and opportunity for a political resolution of a problem," he said "It is a great shame that we have not understood this. This is not a matter for military, diplomats, politicians. This is a matter of collectively failing to exploit the opportunity the military gained."
In a statement later issued by the Ministry of Defence, Sir David said: "The nature of military operations is that need is always balanced against available resources. It is the job of senior military commanders to help the government assess those priorities against the resources available, especially in the current economic conditions. As I have said before, I and the Chiefs of Staff agree that we can deliver the military capability required by the SDSR with the resources available. On Afghanistan, we all agree that you cannot win an insurgency through military means alone, it has always been understood that a political solution will ultimately be required."