Cheika, whose side has now lost four straight Tests, lamented inaccuracies in his team's play.
"I know there will be plenty of people looking to put the boot in, and I'm ready for that," Cheika said.
"But I'll always get back up and as a team we'll come back and try and play that style of footy.'
"The people I feel for most are our supporters. We've let them down." While lauding his side, former Wallabies coach Jones stressed his new team hadn't been at their best.
"We had a number of players sub par, it was a fantastic effort from the squad to beat a very good and determined Australian side," Jones said.
"Our setpiece gave us a significant advantage in the second half and just pleased with the general attitude of the players.
"To win the end of that game was a superb effort.
"They showed fitness, they showed toughness, they were brave. Cheika said the AC joint injury that forced lock Rob Simmons off at halftime and gave Adam Coleman a Test debut, was at the high end of the range, but wasn't sure how long the Reds forward would be sidelined for.
He said he wasn't happy with the refereeing through the series and was disappointed Welsh official Nigel Owens gave a "50-50" ruling when the ball from an England kick hit the wire of the overhead camera tracking the game.
-AAP