Defence Secretary Bob Ainsworth, who is in Afghanistan, said it was vital to the UK's national security, while Army chief Gen Sir David Richards said the death had hardened "our determination to succeed".
Sir David also urged the public not to judge the campaign by casualties alone.
The US, the UK and other Nato countries have announced a surge in troop numbers, but America stressed it would begin to withdraw its military by 2011.
Afghan President Hamid Karzai warned it would take 15 years before Afghanistan was able to pay for the costs of maintaining its own security forces.
British troops arrived in Afghanistan in 2001 as part of a US-led invasion following the 9/11 attacks.
The total number of UK troops killed since the start of operations in 2001 has now reached 237.
'Full of resolve'
Maj Christopher Davies, commanding officer of C (Essex) Company, said L/Cpl Drane was "a thoroughbred soldier with huge potential".
Most recent UK fatalities
Total deaths 2011: 32
Updated: Dec 18 2011
"After nearly two months of almost daily engagements with the enemy, of which the majority were fierce and unrelenting, he remained hardy, focused and full of resolve," he said.
Pte Jason Field, from L/Cpl Drane's platoon, said he was a "kind and loving" man.
Pte Dan Burgess, also in the same platoon, said he would remember "Add" for his love of music.
"When I first met him seven years ago with his long blond hair and bass guitar in hand, I never once thought a few years down the line, we would be in Afghanistan together," he said.
"He will always be remembered as an excellent soldier, and an even better friend."
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