But experienced television match official Glenn Newman ruled Anscombe had not grounded the ball.
An earlier infringement saw Patchell kick a simple penalty as England turned around 12-3 ahead.
Wales conceded two tries in the opening 19 minutes when they tried to play an expansive game in wet conditions but Gatland did not put that down to barbs from his opposite number, England's Eddie Jones, in the buildup when he accused them of being cocky and questioned their experience and bottle.
"I can not understand why the television match official did not award Gareth Anscombe the try", said Gatland of a decision made by Newman, his fellow New Zealander. They were playing at a tempo that Wales were unable to slow: when Josh Navidi did get over the ball, he was dumped on the ground and England picked and ran, getting over the gainline and widening the point of attack. "That looked a clearcut one to me".
"He has one big call to make and unfortunately he's made a awful mistake and at this level that's pretty disappointing", Wales coach Warren Gatland said.
"I can not do much about it now".
"I just struggle on the wording". He said England got there first and there was no downward pressure from Wales. We want to win the Six Nations but we're also using this as a trial for the World Cup, so it's a great opportunity to get some really quality scrum practice in. I allow him to make the decisions.
It was the kind of tackle that epitomised England's desire to preserve their unbeaten home record under Jones and keep their bid for an historic third straight Six Nations title on track.
Wales defended desperately as England battered away for phase after phase but eventually cracked when lock Joe Launchbury off-loaded superbly in the corner to open the door for May to make the short dash to the line.
"We were relentless in punching holes in them and we did that all day here", said May. "That got us the win".
"Any try for your country is very special and it's an awesome feeling to get two important ones in a game as tight as this".
EJ: He's been excellent for 23 tests for us so I don't know what was different today.
"The second one was a brilliant effort from the whole team. It could have been anyone popping up to finish the move off".
Despite Wales clawing their way back into contention with a valiant second-half display after England's fast start, captain Alun Wyn Jones said it had been too little too late. If you don't want me to do it, I won't do it.
Eddie Jones called it an "arm wrestle" and he cut the figure of a man who relished every second of watching his players strain every sinew before the Welsh forearm was finally forced backwards.
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