Wales made light work of the 2018 champion at Principality Stadium, with Hadleigh Parkes crossing inside two minutes and Gareth Anscombe adding 20 points from the kicking tee.
It was unable to hold on for a shutout, though, as Jordan Larmour touched down beyond the 80th minute for Joe Schmidt's side.
England needed Wales to slip up against Ireland to keep its hopes of snatching the title alive and Jones suggested in the build-up to this weekend's fixtures that Gatland's side looked tired.
Speaking after becoming the first coach to win the Grand Slam three times, Gatland said: "It was a fantastic performance and we didn't look too tired, did we?
"I'm proud of the players. It's not about me, it's about those players. We spoke beforehand about the players playing for themselves, their families, the fans and Wales as a whole and being able to create a bit of history. You can never take that away from them now."
Having swept aside all comers in the Six Nations, Wales will likely be considered among the favourites to win the Rugby World Cup in Japan.
Captain Alun Wyn Jones said it had "put a target on our back" with Grand Slam glory and Gatland believes it is capable of overcoming any opponent.
"We'd been trying to slip under the radar. We know on our day that we're capable of beating good teams, so I think we'll have a break now and start preparing for the [Rugby] World Cup," the coach said.
"These boys train exceptionally hard, will run through a brick wall for you. They're a really tight group and really close to each other.
"If we go there with a bit of luck and don't pick up too many injuries we've got a good chance of beating anybody."