The Leicester Tigers winger struck twice in the opening quarter to seemingly put the defending champions on course for a handsome victory.
Anscombe's spot among the replacements was taken by Owen Watkin.
"I can not understand why they haven't awarded the try to Gareth Anscombe", said Wales coach Gatland.
After every game we will always review our performance and see what lessons can be learnt, what we need to improve on, and looking to see if there was anything that we got very wrong in the game plan that we need to go away and practise. "England always have a good pack but we are not scared of going there". "I was really proud of the guys in terms of the effort", Gatland added.
Ahead of the 131st meeting between these two giants of the sport, few could have considered that the pre-match build-up could be bathed in even greater hysteria.
Overall, England are also on a 14-game winning run at home, last losing on their own patch to Australia and Wales in the 2015 Rugby World Cup.
The England head coach heaped the pressure on Patchell, the 24-year-old preparing to start only his second Test at fly half, by claiming that his Wales team-mates doubt he has the "bottle" to cope with the intensity of the occasion.
Not that it was exactly required.
Italy has now lost 13 consecutive matches in the competition.
Turkey condemns bombing in northeast Libya
The UN-backed unity government based in the capital has struggled to assert its authority outside western Libya. Libya descended into chaos after the 2011 uprising that toppled and killed ruler Moamar Gaddafi.
Victory over Scotland on the opening weekend may have come amid numerous errors from the visitors to the Principality Stadium but it nevertheless came as a surprise that the Scarlets-fuelled side could live with international-calibre opponents.
But not one of them is flyhalf Rhys Patchell, whom Jones has promised will be targeted.
It was the size of a TV screen - a metre by a metre-and-a-half - and it had the Italy and England badges in the middle and tasted absolutely wonderful. He's got to get the ball wide and that's going to be a big job for him.
Patchell then missed the chance to reduce the arrears from the floor, and barely a fraction of a way into the contest he must have been hoping that the whole of Richmond upon Thames would swallow him up.
After Farrell had converted, Wales responded strongly and appeared hugely unfortunate when Anscombe looked to have beaten Anthony Watson to a loose ball and scored, only for the television match official (TMO) to rule otherwise.
Gareth Anscombe kicked another three points in the 76th minute to ensure the match was tightly poised during the closing stages, but Wales just couldn't muster enough energy to find that try to win them the match.
The second period started much like the first, with England dominating possession though they were unable to increase their lead despite having regular possession in Wales territory.
Reacting to Jones' comments at Wales' Surrey base on Friday, Alun Wyn Jones said: "It was more important that World Rugby, when they were asked for clarification, came back and essentially said that they saw nothing untoward with what happened".