The vice-captain said falling short on the run count and not keeping pressure up on the hosts led to defeat Down Under.
Anderson stood in for captain Joe Root at the presentation, the skipper put out of action due to a “gastro bug” that followed playing in record heat on the final Test’s penultimate day.
He said: “I think, to be honest, we’ve been outplayed in the key moments of each game. We’ve been in the games to an extent but we’ve just not been able to capitalise on any opportunities we got.”
The 35-year-old added: “Australia - credit to Steve (Smith) and his team, they’ve played fantastically well throughout the series and were the far better side throughout the tournament.”
Australia’s bowlers were unrelenting to the final wicket, finishing off England for 180 runs in the final Test as they scored an innings and 123 run win.
Anderson said: “They have got a fantastic bowling attack and all the batsmen have come to the party, they’ve scored runs when the team needed them.
“I think looking at ourselves that’s were we’ve slipped up. We’ve not scored the amount of runs you need to win a series like this and as a bowling group we have not not created the pressure for long enough periods of time.”
Root, who had spent the morning in hospital with dehydration before returning to the Sydney Cricket Ground hoping to make a final stand, was “asleep in the dressing room trying to recover” when the final wicket fell.
Anderson said: “He’s not been too well throughout the night and it’s taken its toll on him, I think the heat yesterday didn’t help.”
Paying tribute to the England fans who on Sunday endured the hottest day in Sydney since 1939, Anderson said: “We are very lucky to have such great support, not just the Barmy Army, we’ve got a lot of English travelling support that follows us round the world and we are very grateful for them even though we’ve been beaten in this series.”
Australia captain Steve Smith said “belief”, each player knowing their roles and a home crowd were behind their success.
He said: “I think England had their foot in the door in all of the Test matches, they’ve played some exceptional cricket and we’ve just been able to get on top in those key moments and not let them back in the game which has been crucial.”