Clarke's 35th-minute goal look destined to win the League One side's replay against Hartlepool but defender Jack Baldwin drew the visitors level with three minutes to go.
Manager Steven Pressley praised his team's performance and felt, while booking their place in round three was crucial, avoiding the additional 30 minutes was an added bonus ahead of a visit to Swindon at the weekend.
He said: "Our performance was excellent. Their attitude to the game was first class and I was just disappointed we lost the goal just before full-time because Hartlepool, who are a good side, created no real chances.
"After the first goal, we should have added to that and when you are winning 1-0 in a cup tie it's a precarious position and they went and scored from the corner right at the end.
"Our response was excellent. In the last 10 minutes we looked like we might score because of the changes they made but once again it came down to big Leon and what can you say about him?
"He's a striker of phenomenal quality at this level and he scored two very good goals. He's a big player for us and when he is out of the team he is missed.
"His second wasn't just a big goal in the context of this evening but also in looking ahead to Saturday and going to Swindon on the back of 120 minutes of football.
"But I thought it was a really good team effort."