The series ended in a 1-1 draw after a thrilling Third Test ended 15-15 at Eden Park, Auckland, on Saturday morning.
That result means Sam becomes the first Lions skipper to remain unbeaten over successive Test series, having led Lions to victory in Australia in 2013.
It's also only the second time the Lions have avoided series defeat in New Zealand - the only victory back in 1971.
It's also the first time the All Blacks have failed to win at Eden Park since 1994.
The home team dominated the first half but missed opportunities and Lions hung in there at 12-6. Lions pulled back to 12-12, All Blacks then led 15-12 but Owen Farrell responded with a penalty to ultimately tie the match and the series.
Below: The two teams at the trophy presentation
Speaking immediately afterwards, Sam said: "It's difficult as players when you go through all the pressure and the emotion of the week, it's all geared towards winning, but it's better than losing I guess!
"I'm a bit speechless. I don't quite know what to make of it. I was ready for extra time!
"We've come to the double world champs and what they've done here over the years has been incredible so to come here and not get beaten is something we can take credit for.
"It was a great Test match to be involved in.
"There is no indivudual accolade when you are captain. This is a massive team effort. Credit to our team - it has been a privilege to work with them."
Sam - a former schoolmate of Gareth Bale at Whitchurch School, Cardiff - told us how he came to support Spurs back in 2013.
"My father was born in London and brainwashed me and my twin brother Ben to support spurs from age six when I got my first shirt. He would always tell me 'you're Spurs in the blood now boys!' He had supported Spurs most of his life too."
Below: Sam interviewed pitchside at the Lane
Now 28, Sam became the first Welshman to captain the Lions since Phil Bennett in 1977 when he took the armband for the Australia tour in 2013. He performed superbly as Lions won the first Test 23-21 before narrowly losing the second 16-15. He was injured for the third Test where Lions ran out 41-16 winners to clinch the 2-1 series victory.
Capped 75 times by Wales, he first represented his country in 2009. He captained Wales for the first time in 2010 and led them at the 2011 World Cup, where they reached the semi-finals. Wales then clinched the Six Nations' Grand Slam (winning all five matches) in 2012, retaining the title in 2013.