Australia reached 174 for six at stumps on day four in Nottingham and Clarke believes 19-year-old Ashton Agar, who scored 98 in his first Test innings, will play a key role if Australia are to push on tomorrow.
Clarke told Sky Sports: "I'll never give up, especially when we've got young Ashton Agar. He's in really good form and batted beautifully in the first innings.
"We've also got the experienced head of Brad Haddin at the crease and the boys left to come in can certainly play a handy role so I'm still confident if we start well tomorrow we can still win this Test match."
The New South Wales native is now focused on keeping England spinner Graeme Swann in check on a turning wicket.
He added: "There's not much bounce and the ball's quite soft so we need to bat for a long time and use the majority of the day.
"We need to play Swanny well. We're seeing a bit more spin now as the wicket has deteriorated but there are two good players at the crease at the moment."
Clarke also supported England bowler Stuart Broad's decision not to walk on 47 when umpire Aleem Dar failed to spot a thick edge off Agar's bowling yesterday.
Big-screen replays showed clear contact but Broad stood his ground given Australia had used up their two reviews.
"I think it's up to him, there's no doubt about it," Clarke said.
"I've always believed the umpires are paid to make decisions.
"If every batter was going to walk when they hit the ball, we wouldn't need umpires. It's up to individual players to choose to walk when they hit it.
"I certainly don't think any less of Stuart, that's for sure."
England batsman Ian Bell talked of his pride after bringing up his 18th Test century with a stand of 109 before he became one of Mitchell Starc's three victims.
"It's a great feeling to score a Test match 100," he told Sky Sports 2. "You talk about it in the dressing room and it means a lot to everyone in the 11. It's a real proud moment.
"I certainly think in Ashes cricket it was (an achievement) and to play an innings like that in that situation, using some different skills on a slow pitch with a reverse ball, it was different and I really enjoyed it.
"With the ball reversing I was trying to play it as late as possible and the plan was to hit it as straight as possible and to time the ball short. You want to play it as late as possible and use the pace.
"It's been a brilliant Test match and today hasn't disappointed either. It's really exciting to come back tomorrow morning with all results possible."