"It's devastating to lose, but especially after that finish. Even if we had drawn the game it would have been some comfort to take the series to the last game," said Shaw.
"But that was not a nice way to finish - no one was talking in the changing room. Ian McGeechan said we should be proud of ourselves, but it's difficult to lift anyone right now.
"Ultimately we came here to win the series and we've lost. I would rather have been taken off at half time for feeling poorly and the team won than win Man of the Match and lose.
"I was proud to wear the Test shirt, but I wanted to win. I thought we still had time to go for one last penalty and win it, but unfortunately I watched their last kick the whole way and it went straight down the middle - it was devastating."
It was Shaw's 16th Lions appearance on his third tour and his first Test appearance came 12 years after his Lions tour debut.
"We will regroup and hopefully we'll put in another performance we can be proud of next weekend," said Shaw.
"The move to uncontested scrums was the turning point as we had the edge on them in that area. The feelings afterwards are the same feelings I had after the World Cup Final - I'm just absolutely gutted. I can't describe how bad it felt.
"I had worked so hard to get there, but we lost and another video refereeing decision didn't go our way. I just wanted to do myself justice and my selection justice.
"I was the most nervous I ever felt before a Test match. Two days before I couldn't sleep. Usually I don't get like that because I am a very laid back person.
"But I managed to temper those emotions and before kick-off I felt very confident of what I could bring to the game. I think we are all proud of our performance today but in the end we came up short.
"We have earned a bit of respect but losing those two games you will always look back and wonder what could have been or what should have been."