Colin Charvis said Wales felt a mixture of pride and frustration after their one-point loss to the All Blacks.
"We can hold our heads up and feel we put in a performance worthy of the Wales jersey, but the guys are very disappointed," Charvis told BBC Sport.
"We've lost two games against world-class opposition by narrow margins and it's very difficult for us to accept.
"We feel we are progressing but it's imperative we bounce back and get straight into it again."
Charvis and his fellow Welsh forwards were inspirational, and can proudly claim to have got the better of their New Zealand counterparts.
But behind the scrum, the All Blacks were in devastating form as the backs pounced on any opportunity to combine with skill and pace.
They scored three tries of high quality. Two came from winger Joe Rokocoko - the second the pick of game - and the other from full-back Mils Muliaina.
Charvis added: "The All Blacks are one of the world's best. We're striving to achieve that kind of standard.
"When they turned it on they were scoring tries and they did us with some superb handling in their backs.
"I think we gave them a few too many piggy-backs with penalties through our indiscipline, but it was imperative we showed the bounce-back ability during the game to keep going.
"Every time we fell behind we pulled up our socks and carried on."
Wales coach Mike Ruddock said he could not have asked for more from his players, and believes his side proved they are up there with the best in the world.
"The boys are very, very down," he said. "We are all professionals. We want to win every game.
"We are not patting ourselves on the back because we got close. We are disappointed.
"We have to keep working and get that luck. A little didn't go our way at times. We missed a few kicks."