I've studied communist purges a great deal and never have I encountered any instances of Stalin expressing remorse. Likely, the answer is no. I can give you a great many cited instances of him covering up or doubling down on his purge orders, but I've not seen any of the opposite yet in all my reading.

The initial success of Barbarossa has less to do with Stalin's purges and more to do with Stalin ignoring the intelligence that the German attack was imminent. The forces that were to repel Barbarossa weren't adequately deployed and many were in the middle of modernization cycles and were half-equipped. That's not a result of the purges; its a result of the ignoring intel - in a large part because Hitler postponed Barbarossa, which meant the agents who had accurately reported the dates pre-postponement found themselves in the awkward position of having to say: "we know it didn't happen the last two times, but trust us, it's this time for really reals!" The Soviets do issue an order for their troops on the border to prepare for an invasion on the eve of Barbarossa, but that's not much use when nothing's been pre-positioned.

Stalin did seem to experience some kind of regret or breakdown over the USSR's lack of preparedness; According to Soviet Foreign Minister Vyacheslav Molotov, after a fraught meeting at the Defence Commissariat on June 28, as he returned to his official car, he supposedly burst out "Lenin founded our state, and we've fucked it all up!" and continued ranting in this vein all the way back to his dacha. He then shut himself away for two days and stopped answering his phone. Was this because he had snapped? Or was he just testing the loyalty of his lieutenants, as Ivan the Terrible had done hundreds of years earlier? [X-Files theme plays].

Simon Sebag Montefiore, in Stalin: The Court of the Red Tsar, suggests probably both, and that's the source for the above paragraph by the way.