Steve Smith's Australians swept to an innings victory in Monday's final Sydney Test, condemning England to four comprehensive defeats in the five-match series.
Vice-captain Anderson, deputising for stricken skipper Joe Root, said the writing had been on the wall for some time.
"Weve known for a few weeks they're going to lift the (Ashes) urn, but I guess, seeing them do it in person is tough to watch," Anderson told reporters.
"There's not a lot we can do about it. We've not played well enough and they've deserved to win.
"Just got to give them credit and they're well within their rights to be over the moon with that win."
Anderson, 35, who is England's all-time leading wicket- taker with 523 in 134 Tests, said the tourists were unable to make their moments count during the series.
"I do think it's been closer than 4-0. We've been on top in some games, if not all the games at some stage," he said.
"We've just not capitalised on the key moments where if we kick on with the bat and get a big score in the first innings then we've put them under more pressure.
"Similarly, if we get them a few wickets down early, then a couple more would get us in the game and get us on top.
"They've played those pressurised moments and those situations better than us.
"When they've done that and put the pressure back on us, we have not coped with that very well and that's why they've won."
Anderson, who toiled away for 223.3 overs for 17 wickets during the series, said the tour outcome was galling for the team.
"All the guys in the dressing room are hurting. I'm sure they're hurting as much as I am. That feeling that you get should make you determined to win the Ashes back in 2019."
Looking ahead to the Ashes series in England next year, Anderson said he was "hungry" to play.
"I'm going to do everything I possibly can be to be ready for that series in 2019. I'm still hungry to play," he said.
"I'm delighted Ive got through these five Test matches and bowled pretty well.
"I'm going to go away now and have a few weeks off and get ready for New Zealand in March.
"I'd never really liked looking too far ahead, but I'd still like to be around in 2019.
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