Pritchard, making his home debut on a season's loan from Tottenham, saw his 56th-minute spot-kick saved by Torquay goalkeeper Martin Rice who dived to his left to parry.
But caretaker boss Cooper is confident the England Under-20 international will not let the blunder dent his confidence.
Cooper said:" We have that many good technical players here that I have a bit of a fight as to who takes penalties.
"In training Pritchard took about 10 of them and smashed them all in the opposite corner, so I have no worries about his ability to take them."
Pritchard was brought down by defender Lee Mansell to earn the penalty and after he had failed it looked as if the match might go to extra time.
But, with seven minutes remaining, Swindon substitute Miles Storey got away from the Devon club's defence and his low centre was turned in by Williams.
Cooper was quick to praise local teenager Storey who came on in the second half and made a major difference with his pace and control.
"Miles Storey added zip and zest and was a real threat to their goal," Cooper added. "Williams is claiming the goal from close range but I wondered at the time if it might be offside.
"As to the next round, it is fate that we shall get Sunderland and Paolo Di Canio."
- Sports & Recreation