The tourists will begin day five at Trent Bridge on 174-6, requiring another 137 runs for victory.
Clarke knows that his side will have to bat incredibly well in order to stand a chance, but the skipper has the utmost confidence in Ashton Agar and Brad Haddin, who ended day four with an unbeaten partnership of 10.
Clarke told Sky Sports News: "I will never give up, especially when we have got young Ashton Agar, who is in really good form and batted beautifully in the first innings, and the experienced Brad Haddin at the other end.
"I think the other boys left to come in can certainly play handy roles so I'm still confident if we can start well tomorrow morning we can still win this Test match. There's not much bounce and the ball's quite soft so we are going to have to bat for a long time.
"We are going to have to use the majority of the day to make the runs - there's no doubt about it - and play Swanny well. I think obviously we are seeing a bit more spin now the wicket has deteriorated but we've got two good players at the crease at the moment."
Haddin, who has 10 Test 50s and three centuries to name, made just one off two balls in the first innings. Meanwhile, batting at number 11, Agar marked his Test debut with 98 off 101.