Royal United Services Institute said the RAF nearly ran out of a key missile and the Royal Navy had to curb other commitments to deploy warships.
It also said the UK and France each had 40 special forces troops on the ground.
But Defence Secretary Dr Liam Fox said: "Operations in Libya have... shown that we retain our global reach."
The two countries' leaders became "accidental heroes" after the success of the campaign, the think tank added.
The institute said UK Prime Minister David Cameron and French President Nicolas Sarkozy, who pushed Nato to launch air strikes, received a rapturous welcome on a visit to Libya last week.
The UK and France deserved "credit" for their efforts, the report argued.
'Messy and ambiguous'
Operations are still ongoing in Libya, with Nato saying it will extend the air campaign for up to 90 days.
The country's interim rulers, the National Transitional Council, say their forces have now taken control of much of the southern city of Sabha, one of the key remaining strongholds of Colonel Gaddafi's supporters.
This initial assessment of the Libya operation praises the actions and determination of Britain and France in seeing the mission through.
But it highlights uncomfortable questions over launching a war on a second front against a backdrop of painful defence cuts.
There is no doubt Britain played a key role in Libya. But it's also clear the nation's armed forces were stretched.
At one stage the RAF was running low on one vital weapon - the modified brimstone missile.
While the UK managed without an aircraft carrier, three other nations deployed their carriers and provided "unique advantages".
There are questions over the decision to scrap Nimrod maritime spy planes.
The costs of the operation may end up being modest compared with Afghanistan, but the armed forces will still have to pay a price in plugging the gap of lost capabilities and neglected training.
The success of the Libya campaign - assuming it ends in the near future - is clearly not down to careful planning. Britain and France were reacting to fast moving events.
There was, and still is, ambiguity about the mission - with the National Security Council "flip-flopping" as to whether the goal was protecting civilians or removing Col Gaddafi from power never part of any UN mandate.
Mr Cameron and Mr Sarkozy's visit to Libya last week, to demonstrate support for the fledgling new government, came less than a month after the final overthrow of the former regime.
But Prof Michael Clarke, director general of the Royal United Services Institute, said: "Prime Minister Cameron and President Sarkozy became accidental heroes in a civil war, justified - unlike most civil wars - on grounds of principle.
"Like all military operations, this operation was more messy and ambiguous than politicians like to admit.
"In this particular case, it reflected a number of new, and sometimes novel, political and military elements."
The allied operation overcame "big political risks", as well as "the improvised use of weapon systems and ambiguous command arrangements" to find success, the report said.
However, the mission has raised questions about the cuts in forces and equipment announced in last year's Strategic Defence and Security Review, according to the institute.
The report said: "The 'carrier debate' in Britain will almost certainly be reignited by this operation.
"The fact is that the operation was successfully conducted without a British aircraft carrier being available.
"But it is equally a fact that the operation involved four major ships that were capable of launching aircraft - the French, and Italian carriers, the US assault ship, and Britain's HMS Ocean acting as a helicopter carrier.
"British operations in Afghanistan were not affected by commitments to the Libyan theatre, but both the RAF and the Royal Navy had to divert assets from other tasks to cope.
"This crisis demonstrated that the forces could improvise and 'could cope' even in light of the defence review.
"But it also demonstrated that there are significant opportunity costs in doing so and that even a comparatively small operation such as this puts the forces under some considerable strain."
The report draws parallels between the Libyan operation and the 1999 Kosovo intervention, saying it appeared to be "a throwback to some of the crises of the 1990s".
Libya has been different from Iraq and Afghanistan missions where the "emphasis was always on numbers of 'boots on the ground"', the think-tank added.
The report also discusses the activities of the UK's special forces and estimates that in June there were as many as 40 elite troops on the ground, including the SAS. They were involved in gathering intelligence and identifying targets, it said.
But there was still "much to analyse" from the operation and "many lessons will doubtless be derived from it", it said.
Dr Fox said: "Operations in Libya have vindicated decisions taken in the SDSR (Strategic Defence and Security Review) and shown that we retain our global reach.
"The Royal Navy, Army and RAF have all reacted superbly to the recent events in Libya which, in turn have demonstrated that the government's decision to adopt an adaptable posture with flexible armed forces was correct.
"From the very beginning, the UK has been at the forefront of the military operation to protect Libyan civilians and our Armed Forces have had considerable success in doing so working as part of a Nato-led alliance," he added.
Source: www.bbc.co.uk
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