Britain has about 7,000 troops in Afghanistan, rising to 7,700 within months, and is involved in some of the fiercest fighting.
Browne said he was “encouraging” Nato allies to provide more soldiers.
However, “the answer is not to flood this country with troops,” he said.
“What we are doing is building up the domestic troops, building up the Afghan forces in order to take over from us.”
The committee said: “It will require a sustained military and financial commitment by the international community, working with the government of Afghanistan, to create the environment in which enduring democratic institutions can be established.
“If that commitment is to succeed, its size and strength must be very great, and in our view considerably greater than the international community is at present willing to acknowledge, let alone to make.”
The criticisms echo complaints that the US, Britain and Canada have borne the brunt of the combat operations while countries such as France and Germany have been unwilling to put their soldiers in the line of fire.
“We remain deeply concerned that the reluctance of some Nato members to provide troops for the Isaf mission is undermining Nato’s credibility and also Isaf operations,” the committee said.