Hooker Rees was part of an all-Lions front row alongside props Gethin Jenkins and Adam Jones in a pulsating encounter in Cardiff.
And Rees, who skippered his country for the third time in a month against the world's leading nation, has told his fellow players Wales need to make less errors the next time they face the likes of the Springboks, the Wallabies and the Kiwis.
"We have played the three top teams in the world and from our point of view we have been able to match them up front physically and we have kept them in the game for long periods of time," said Rees, who started the second and third Tests for the Lions in South Africa a year ago.
"I think we're disappointed and frustrated, to be honest. We know at this level the difference is errors and until we cut them out in our game, it's going to be difficult to get results.
"I don't think we had the best of starts but we got back into the game at 13-12. One of the biggest things was turnover ball and they capitalised on that.
"They were more clinical than us. I thought their attack was very good off turnover ball and that was the difference, really. I also thought their defence was very good and that's what wins you games.
"We're definitely disappointed because we thought we could take this game. It's important that we learn from the lessons from the autumn series and we'll front-up come the Six Nations. We've just got to keep on working hard."
Wales were within striking distance of the world's best team for the majority of the match but were eventually outscored by five tries to one.
A classy individual effort from full back Mils Muliana was sandwiched between a brace from Hosea Gear, before late scores from Isaia Toeava and John Afoa ended any hopes of an historic victory for a Welsh side who haven't beaten the All Blacks for 57 years.
Lions tourist Lee Byrne claimed a consolation for Warren Gatland's men but it was the All Blacks who completed a third Grand Slam in five years over the Home Nations.