The Saddlers hung on until the 84th minute with brave and resolute defending keeping the visitors at bay.
But after failing to take the few chances they did create, former Wolves winger James Henry pounced to put The U’s 1-0 up.
It was the only goal of the game as Oxford progressed to the third round.
And Clarke admitted they were the better side.
“Oxford were the better team,” he said.
“They’ll be a top six League One team, they move the ball very well.
“And we knew that before the game.
“We were trying to think of a different way to skin a cat.
“My players aren’t at their level, anywhere near it to be honest at the minute.
“But I think effort, endeavor, desire from my lads was there to see.
“Putting bodies on the line.
“There’s still three chances to score the first goal, you’re not going to get many with the amount of possession Oxford get.
“You have to take the most of those.
“If you manage to sneak in front then it gives you something to hold on to.
“Like I say, the effort and application was there for all to see.
“It’s those little bits and pieces where you’re hoping to work them on the counter attack.
“We changed things around shape-wise and had a look at different things to try and skin a cat a different way.
“Unfortunately it wasn’t to be.”