The Well beat the Championship club 2-1 at Almondvale Stadium thanks to a goal either side of half-time from Bob McHugh and James McFadden after Jason Talbot was sent off in the 65th minute.
"I have to say, I thought Livingston were terrific and it was only really when they went down to 10 men that we had chances to kill it off,” said McCall.
"I think we did enough to win the game. I'm disappointed to lose the goal but overall we're in the next round and that's the main thing.
"The park was really wet and it was skidding off and things weren't coming off in the final third for both teams, but I'm pleased James got on the scoresheet and got a full 90 minutes.
"He is desperate to do well, he puts everything into training and games.
"Both strikers scored so that was great."