Billy Mckay's first-half double was enough to ensure that Caley stay at the top of the Scottish Premiership, while the Jambos were unable to continue eating away at the point-deduction.
"I actually thought we started reasonably well, we passed well. Maybe I'm a bit disappointed not to have been as effective in final third, but I thought they perhaps scored the first against the run of play," Locke told reporters.
"Second half they were certainly better team. We just have to take it on chin, work hard and hopefully get everyone available for Celtic.
Hearts are nine points behind St Mirren at the foot of the table, but have shaved seven points off the 15 they were deducted for entering into administration.