The British and Irish Lions received a muted reception when they arrived back in Britain after their series whitewash in New Zealand.
Woodward's team were handed a crushing 3-0 series defeat
A small crowd gathered to applaud Sir Clive Woodward and his players and staff when they arrived at Heathrow.
It was in sharp contrast to the scenes when England came back from the 2003 World Cup and thousands had gathered at the same airport in the early hours.
The Lions lost the final Test 38-19 to New Zealand on Saturday.
The All Blacks were dominant throughout the series as they swept to a 3-0 win and the Lions can expect more criticism over their pedestrian displays.
Their poor showing has led to doubts over the future of the Lions - a touring team drawn from England, Scotland, Ireland and Wales.
But Woodward described as an "over-reaction" suggestions the Lions cannot survive in the professional era.
"The Lions is different in the professional age, it is almost a romantic team rather than a built-up team," he added.
"New Zealand are a very, very good team and it is difficult to bring together four sides very, very quickly.
"It makes it clear a fully professional team will always beat 15 individuals when you only have that amount of preparation time.
"But when you get the chance you should always go and do it. The upsides outweigh the downsides.
"I still think the Lions is a great concept.
"The supporters over there were just fantastic, they have all had a great trip and hopefully they will do again in South Africa in four years time."