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.
The Ashes were relinquished by the third Test in Perth and England gave the impression by the final day of the series that they just wanted it all to end.
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.
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"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.
"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.
"After Perth we were all bitterly disappointed as we had come over here thinking we could challenge Australia and to be three down after three Tests was not where we wanted to be," he said.
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.