Another rearguard action at Old Trafford fell short as the visitors triumphed by 185 runs to ensure the famous trophy will remain Down Under.
Root told Sky Sports: “I thought we showed great character, great fight and great belief in what we wanted to achieve.
“As last week we always believed, we always make sure we fight right until the end and we tried our hardest today.
“You can always look at different areas where you could have done things slightly differently but I couldn’t be more proud of the effort the guys put in today.”
A strong ninth wicket stand between Craig Overton and Jack Leach had briefly raised hopes of another stunning England escape, and Australia captain Tim Paine hailed his side’s resilience.
Paine said: “I was really proud today with how our bowlers kept sticking at it.
“This team’s been through a lot in the last 12 to 18 months and I think the character we’ve shown to bounce back – even from Headingley – shows a lot about the character of the people we’ve got in our side.
“It’s been an unbelievable series, it’s been intense, every game’s gone pretty much down to the wire and that’s what we expected and prepared for.”
Australia’s batting talisman Steve Smith said the victory would take the pressure off the final Test at The Oval, in which England can now do no better than level the series.
Smith said: “There’s another game left and we’d love to win it but to know it’s coming home is extremely satisfying.
“The boys were getting a bit tight out there but with the new ball we thought we’d get enough chances.
“I’ve been here a few times when things haven’t quite gone our way [so] to come back and get the urn here was always one to tick off my bucket list.”
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