The Jambos conceded to Liam Fox five minutes into the second half before Jamie Hamillâ€™s 61st minute penalty levelled it at Starkâ€™s Park which eventually saw the game into extra-time and subsequently to a penalty shootout.
Hearts managed to edge their Championship opponents 5-4 in the shootout and Locke was content with progressing to the third round despite the scare.
"It was certainly not what we wanted, with it going to extra-time,â€ť said Locke.
"We did not do too well in the first half but the second half was a lot better. They got everyone behind the ball when they went down to 10 men (after Dougie Hillâ€™s sending off in the 74th minute).
"We're delighted to be through, the boys' character was fantastic."