Joe Root believes England "outplayed" Australia in Melbourne despite being unable to force victory on the final day.

Thwarted by a lifeless pitch and another outstanding display of batting by Steve Smith, in particular, England had to settle for a draw at the MCG. But while that result at least ends talk of another whitewash, Root admitted to some frustration at not being able to clinch a win.

And while he accepted that England had been outplayed in the first three Tests, he hoped that the improved showing in Melbourne would provide the injection of confidence which could help them win the final Test in Sydney.

"I thought we outplayed them this game," Root told BT Sport. "I know it's a draw but it's something to move forward with and come away from Sydney with a win. We have to go one better there.

"It's been a tough tour and we've been outplayed in three games. But to come off three very difficult games and put in a performance like that is very pleasing. It's a fairer reflection of where we are as a side.

"Finally, we've proved, more than anything to ourselves, that we are a good enough side to compete over here and it's such a shame that it's taken until now. But we've always known there wasn't much between the sides and that's the really frustrating thing for me. We are a better team than we have shown on this trip

"It is frustrating that we have not managed to force a win. We did everything we could on a very flat wicket that was not offering the bowlers very much at all. There was no pace and no spin and if we played for another four days it would be exactly the same. We exhausted every option."

Root was particularly pleased with the character and effort shown by his team. After the disappointment of relinquishing the Ashes at Perth, England saw Australia rush to 122 without loss not long after lunch on the first day in Melbourne. It seemed, at that moment, as if Australia might steamroll England over the last portion of the tour.

But instead, England took a first innings lead as Alastair Cook emphatically returned to form. And while the bowlers had little job in the fourth innings, Root could not fault an effort which saw James Anderson deliver 59 overs in the match.

"On that wicket to get them 327 all out in the first innings was a great effort from our bowlers," Root said. "After the start Australia had, to get back into that first day and produce the two sessions we did showed real courage and skill.

"I'm very proud of the way we went about it. There was obviously a lot of disappointment leaving Perth. We knew we had underperformed and a lot of guys had points to prove.

"But I would never question the character of our squad. The way we apply ourselves, the application and attitude is always there. To put in a performance as good as that is extremely pleasing for me as a captain. You can see the desire is there and knowing we can make big scores and bowl Australia out on an unresponsive wicket will give the guys a lot of confidence."

Root was especially pleased with the return to form of Cook. Cook bounced back from a grim run which had seen him fail to reach 40 in 10 Test innings by becoming the first England player to carry his bat in a Test this century and registering the highest score in history by an overseas batsman at the MCG.

"He's looked as good as I've seen him for a long time," Root said. "He's renowned for his concentration but the way he struck the ball, especially down the ground, that's as good as he plays. At no point did he look flustered or out of control. That is as well as I have seen him drive the ball for a long time."

Root also had encouraging words for Moeen Ali who is now averaging 135 with the ball and 19.42 with the bat in the series.

"Moeen has struggled this week but he is a fine player," Root told the BBC. "Like other guys, he has proven before when it is not going his way he is able to wrestle it back in his favour. He will have a big future for England. It is important that everyone knows that."

George Dobell is a senior correspondent at ESPNcricinfo