The Lions have been criticised for their first Test display, when they crumpled under pressure from a superior All Blacks pack and produced a very disappointing line-out performance.
But the Northampton hooker knows only too well what it is like to feel the critics' wrath.
Thompson was in the firing line at Twickenham last year after Ireland ended England's long unbeaten home record - it had stretched from the 1999 World Cup - partly due to them losing 11 line-outs on their own throw.
The Lions managed eight line-out malfunctions in Christchurch last Saturday and, although Thompson only appeared as a second-half substitute, the unravelling of such a critical set-piece area underpinned an emphatic 21-3 defeat.
"It is like the Ireland match when they won at Twickenham in 2004, it's exactly that," he said.
"On that occasion, it was the same problems in the line-out, and I put my hand up for that, but we came back from it and beat Wales in our next game.
"It is frustrating. There is nothing worse when you are part of a squad and you are losing games, especially like last weekend, when you are so cold sat on the touchline.
"It's always hard going on when the game is like that, especially in those sort of conditions. When you sit on the touchline, you are the best player in the world sat there, it is when you get on the field that matters.
"We have got to feel the pain and take that into this match, but last weekend has gone now. There is a new team this week, and we have got to go out there and put it right."
Woodward put the Christchurch defeat top of his rugby disappointments list, and he remains convinced the right team was selected, just that it did not produce when required.
The Lions had also shown signs of getting their act together, beating Wellington and Otago convincingly before arriving at Jade Stadium, but then it all went wrong.
"There is nothing worse than building slowly and things were getting better and better, when suddenly, that happens," said Thompson.
"You feel deflated but we knew there were going to be highs and lows on this tour, and it is how you pick yourself up.
"We picked ourselves up after the Maori match (the Lions lost 19-13), and now we have got to pick ourselves up again.
"We are all professional players, and we were all absolutely gutted, but the boys got the show back on the road with their performance against Manawatu on Tuesday."
The Lions will be under new leadership, with Wales' Six Nations skipper Gareth Thomas taking over from an injured Brian O'Driscoll and wearing the number 13 shirt O'Driscoll filled for just 77 seconds' competitive action before an All Blacks spear-tackle ended his tour.
And Thompson has been impressed by a player whose infectious personality and undoubted desire to succeed will be vital in the series-salvaging mission.
"There is only one Alfie (Thomas' nickname), thank God! You have got to respect him for the man he is, and what he has done," said Thompson.
"Wales have been through some really hard times and stuff, and fair play, he has come through that. He is a great man for the job.
"Everyone says about making lifetime friends on a Lions tour, and that has happened. You feel part of something special, so what happened last Saturday makes that worse.
"In that sort of situation, it is quite easy for things to crack and start falling apart, but it hasn't. Things have got even tighter, and that is what excites me."