Following a goalless 90 minutes, Bees goalkeeper Richard Lee saved three spot-kicks in succession from Johnnie Jackson, Therry Racon and Kyel Reid, leaving Brentford striker Gary Alexander to score the winning penalty.
Parkinson said: "I was pleased in as much as we'd put in a much better performance than our last game. Penalties are something of a lottery but you just ask the boys to hit the target which is what they did.
"You can't legislate for three fantastic saves like that and fair play to their keeper, they were brilliant stops.
"I was pleased with the work-rate but when you're in a cup situation you are always hoping you might get that bit of luck to carry you through. It wasn't with us but having said that their keeper's saves were out of this world.
"It sounds like a cliche but now we can concentrate on the bread and butter of the league and make sure we push for promotion."
Source: PA
Source: PA