Tough conditions made for a grizzly encounter at St Mary's, where the visitors twice came from behind to eke out a 2-2 draw.
Saints took an early lead through a wonderful Rickie Lambert free-kick, only to be pegged back by Peter Odemwingie's first goal for Stoke, who had gone 369 minutes without netting away from home before that.
Steven Davis' fortuitous effort saw Saints retake the lead soon after, but they again relinquished control when former Southampton frontman Peter Crouch bundled home.
Saints continually pressed for a winner in the second half but could not find a way through, much to the annoyance of manager Pochettino.
"It is not frustrating, but disappointing," the Saints boss said. "Over the 90 minutes we deserved to win but in football you can't really deserve to win you have to show it and do it.
"The only 'but' is that after that [Lambert goal] we were not aggressive enough to go on and get a second and that would have put the game to bed.
"Then when we went to 2-1 we weren't able to hold on to the lead and again we should have been more aggressive.
"We practically nullified Stoke in the second half and were creating all the chances but in the end it was not to be."
Saints have now gone five matches unbeaten in the league, but three of those have ended as 2-2 draws despite Pochettino's side edging them.
"Both against Arsenal and Stoke the game ended 2-2 and we deserved more, but overall we're on the right path," he added.
"We were playing against most physical team in Premier League and the weather conditions were difficult so overall we have to look at the positives.
"We had full control of the game, especially in the second half. Stoke are a team who play to their strengths and I have full respect for their approach to football. But we deserved more from this game. "