The Quakers dominated the chances in the opening 45 minutes, often getting a 3,000 strong crowd off their feet.
But after some resolute defending, Walsall finally got the breakthrough just before the 70th minute.
Striker Caolan Lavery netted his fifth of the season when he met Rory Holden’s corner with a powerful header.
The Saddlers then controlled the remainder of the game as kept hold of their lead.
And Clarke was pleased that his players are starting to find different ways to win games.
“Let’s be honest, it wasn’t a classic,” he said.
“I thought Darlington are a credit to themselves over the two games.
“Really hard fought, never gave in.
“I thought first half they probably edged it, I wasn’t too happy with the first half.
“But second half I thought we were in control, albeit while not creating too many opportunities.
“A well worked set piece and we saw the game out comfortably in the end.
“It’s about winning football games.
“I called the players mentally soft in our bad run in October but now we’ve won three games on the spin and shown a different side to us.
“Hopefully the boys are learning how to win football matches, there’s loads of different ways you can win games.
“Sometimes you have to roll your sleeves up and try and quieten down a hostile crowd that got right behind the club from minute dot.
“We’ve come here, pitch is bobbly, their players are giving everything and raising that 10, 15 per cent.
“But my lads found out a way to win, which I’ve been asking of them on a consistent basis.
“I’ll rewind to exactly what I said in September when we won four on the spin, we’re a million miles away from where I want to get us as a football club.
“But what I will say is, if players can come out of the October spell, they’ll come out as better players.”
The Saddlers now host high-flying Oxford United in the second round of the competition.
The League One side sit seventh in the division and they will travel to the Black Country for the tie at the end of the month.