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. "
The result brought an end to Stoke's four-game losing streak away from the Britannia Stadium and was a decent follow-up to last weekend's 2-1 win against Manchester United.
"It was an important game for us," manager Mark Hughes said. "Obviously we had a fantastic result last weekend against Manchester United and it would have been a real disappointment not to have got something out of this game because it is important we get a run going.
"I felt we were the better side in the first half, albeit we went behind twice, but we showed great character and no little skill to get back on level terms.
"In the second half, both teams cancelled each other out somewhat and as the away team that's a very good performance from our point of view.
"They're a team I've enjoyed watching this year and we restricted them to very few clear-cut chances. That shows the quality of our performance."
Charlie Adam was again key for Stoke, following up his winner against United by providing the assists for both goals at St Mary's - the first a particularly impressive through-ball for Odemwingie to net.
"He's got that, we all know that," Hughes said of the Scotland midfielder. "What we have now is a little bit of difference in terms of our attacking threat.
"Peter Odemwingie has joined us and he's an experienced Premier League player and we've talked about him exploiting that space in between centre-backs behind full-backs and Charlie, given his range of passing, will always put people through."