The Cobras took the lead in the 14th minute through Joe Massey who produced an excellent finish to score from a Connor Wright cross.
However, the home side were unable to build on their early advantage and were made to pay when St Andrews equalised in the 42nd minute through a Joe Linley free kick that took a deflection off a defender in the wall.
Despite both sides creating chances in the remainder of the game, it went to penalties where Clipstone debutant Charlie Bryan produced a fantastic stop to keep out Linley’s penalty, but Ethan Blackbourn and Josh Pickering were unsuccessful with their spot kicks.
And Clipstone boss Dave Hoole thought his side deserved more.
He said: “It’s disappointing as I thought there was only one side in it, if I’m honest.
“They’ve got a deflected goal and we’ve missed a lot of chances so it shouldn’t really have had to go to penalties, especially as Jack [Warwick] has gone through on goal at the end but his finish has let him down.”
“So we’ll need to work on our finishing. Penalties is a cruel way to go but we all know what they’re like and all the best to St Andrews in the next round and for the rest of the season.
“We’re scoring some good goals – we watch them back when have videos of the games and it’s one touch football at times and we work it really well both off the ball and when we’re in possession and the movement in the box is great.
“But once again it’s what we’ve talked about in terms of players not peaking in every single game and we need that consistency as it’s a bit of a roller-coaster ride with the players that we’ve got – if we can get the consistency we’ll be up there and we’ll be fine.”
The Cobras are now at home to Retford FC this Saturday with a 3pm start.
Hoole added: “We need to get the lads upbeat as it’s not nice going out of a competition on penalties, especially when we were the better side for most of the game against a team doing well in their own league.
"But we’ll work on a few things in training and aim to put things right on Saturday.”