The Lions, who conceded their highest points total in a Test match against New Zealand, Australia or South Africa, must now pick themselves up for next Saturday's Auckland finale.
Welsh star Thomas though, who took over leadership duties from an injured Brian O'Driscoll, was delighted with his players' efforts.
"There is so much history involved with the Lions, so much history behind the badge, and we can take a lot from this - we can be proud of our performance," he said.
"It's all about getting together now, knuckling down and getting things together for next weekend. The All Blacks probably played a perfect game, but I suppose it's because they are capable of doing it and capable of repeating it.
"It's up to us now to go away, analyse the game and come back with something special in Auckland next weekend.
"We have taken a lot of criticism and a lot of stick, and I am just proud of what the guys did. The scoreboard really is irrelevant to me."
Lions full-back Josh Lewsey conceded that Carter and company had undoubtedly established themselves as world rugby's team of the moment.
"In terms of next week, we've got to go out there and basically come off the field with our heads held high," said Wasps ace Lewsey.
"Gareth Thomas said before the game you don't fear losing to a better side, but what you do fear is not fronting-up, and we gave it everything. We were beaten by a better team.
"Carter's performance was one of the best displays by a fly-half I have seen for a very long time, especially at that level, but I don't think you can just single out him.
"All the (New Zealand) players had the mentality to attack from everywhere, and if you play a game like that in conditions like that and manage to have a low error-rate, which they did, then your defence is going to be put under an enormous amount of pressure.
"They are the best team in the world at the moment. They reminded me of Wales this year in the Six Nations, and they reminded me of England two years before the World Cup.
"Fortune favours the brave, and it was a lesson in how to play modern rugby."