After overcoming early Wales pressure and a head injury assessment for Dylan Hartley, which the skipper passed, England moved ahead in the third minute as Wales was caught cold after Rhys Patchell's failure to collect a box kick from Danny Care.
However, television match official Glenn Newman decided there had been no clear grounding by either defending Anthony Watson or Anscombe, a decision Gatland clearly disagreed with.
"We have not been afraid of going there (Twickenham) since I have been involved", said Gatland.
"It is a pivotal moment in the game".
"The TMO has one big decision to make and unfortunately he's made a bad mistake". "When he tried to stop the referee from allowing the kick at goal - we can't have that in the game", the former Wallabies coach said. I just struggled with the wording (heard on the Ref Link).
Australian coach Jones has won 23 of his 24 Tests in charge of England following his appointment after a 2015 World Cup where a Twickenham defeat by Wales played a key role in the side's first-round exit.
"Well, I saw that completely different. It's human error, he makes a mistake, but at this level in front of 82,000 people when there's a lot at stake guys have got to get those decisions right".
"Shaun has been banging the drum with regard to putting them under pressure", said Wales forwards coach Robin McBryde. You can not do anything about it.
TMO stands for Televised Match Official, a referee who sits in a remote location outside of the stadium looking at controversial decisions on a video replay.
Wales came into this Six Nations clash with confidence, having smashed Scotland 34-7 in Cardiff last weekend, but England showed why they are favourites to claim a third consecutive Six Nations crown with a hard-fought victory.
"I have never made a comment on a TMO", Jones said.
These marginal inaccuracies, and England's more clinical execution by contrast, was one of the big differences on a night when Owen Farrell and Mike Brown excelled. "We've lost Dan Biggar and other guys".
But England fouled at the breakdown and were lucky not to suffer a yellow card.
"We got inside their 22 a number of times, but couldn't unlock them".
Farrell converted and England were good value for their 12-0 lead.
May then latched on to a fine one-handed offload from Joe Launchbury midway through the opening half to double both his and England's tally.
But Wales could have had two tries, too.
"It's a win built around courage and belief", said Jones.
If England appeared to be winning the battle of the defences, then there was no doubt they were in the ascendancy going forward through the first 40 minutes. "It's the one you get up for, you think about all season and it's coming this Saturday". We have to continually remember that.