"If we can level the series we will take a lot of confidence back to Australia," he said.
Australia need to win the fourth Test at Durham, starting Friday, and the final Test at The Oval, on 21 August, to draw the series.
"I'm confident if we play the type of cricket that we have through the four days here that we will give it a real good shake.
"We've got some work to do over the next few days to make sure we are as well prepared as we were leading into this Test match. We need to play with the same attitude, intent and I'm confident we can have success."
On the final day, they reduced the hosts - chasing 332 to win - to 37-3 in their second innings when rain washed out the rest of the match to give England the draw they needed to keep the urn.
"It's unfortunate from an Australian perspective and all the boys in the room are quite disappointed with not being able to get over the line today," Clarke added.
"But I certainly don't want to take any credit away from England. They outplayed us in the first two Test matches, especially at Lord's.
"You know when you come to the UK there is a chance that rain is going to play a part throughout the series. Getting ourselves into the position of being 2-0 down - it was always going to be tough coming back from that."
Australia tinkered with their batting order in the second innings at Old Trafford, promoting David Warner to open and dropping Shane Watson to number four.
Clarke hinted that Watson, who averages 24.33 from six innings in the series, may have to accept a role down the order in the Durham Test, which begins on Friday.
"It's a tough one. It's working out what is best for the team and give Watto the opportunity to play where he feels most comfortable and give the team the most success," said Clarke.
"If he's scoring runs and taking wickets it goes a long way towards helping us win Test matches. We'll continue to talk and assess what's the best for the team.
"Shane understood my reasoning for opening the batting in the second innings and was more than happy to move to number four, and has made it very clear that wherever I would like him to bat he will certainly do that for the team."
Clarke's brilliant first-innings 187 in Manchester is the only century by an Australia batsman in the series, but he insisted the side were not dependent on him and backed his team-mates to fire in Durham.
"I'm just like another player - I'm another batsman in the team that needs to make runs," he said.
"When it's your day you need to make the most of it and I got a bit of luck in the first innings.
"It was nice to make a big score. I think everybody is working just as hard. I think we'll see some of the other guys make big hundreds as well."
Listen to the Test Match Special podcast as Geoffrey Boycott and Jonathan Agnew review each day's play.
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