After enjoying the better of the first hour at the Stadium of Light, Saints fell behind when Phil Bardsley's shot cruelly deflected off Jos Hooiveld to give the Black Cats a scarcely-deserved lead.
Pochettino threw on James Ward-Prowse and Jason Puncheon, and the change had an immediate effect as the former set up the latter for a 76th-minute leveller.
"I think we even deserved a bit more than a draw, looking at how we played today, but that's been happening in our last few games," said the gaffer at full time.
"We dominate large parts of the game and keep possession, but we're having a little bit of trouble scoring.
"I think we dominated during large periods of the game today and we played a very good match, but in the Premier League it is not enough just to play well.
"You have to actually certify your wins by scoring more goals but I think that in the Premier League – like the Spanish, Italian and many other European leagues – in the last ten games of the season it is very hard to score.
"You have to have the mental capacity in those games to know how to score goals because they are very different to those at the start of the season.
"We're very lucky that the two substitutions had an immediate effect on the game," continued Pochettino.
"They created the inter-play between them, and Punch was able to score the goal.
"It is pleasing that both substitutes that came on had an immediate effect - that happens occasionally, but also the opposite could have been true!"
Saints now have a five-point cushion from the relegation zone, meaning only a dramatically heavy defeat to Stoke on the final day of the season could leave Pochettino's men in any danger of relegation.
And, while the manager was in no mood for reflection come full time, he did admit that he will now step up the preparatory process for a second campaign in the Premier League.
Saints could still finish as high as 10th if they see off the Potters next Sunday and results elsewhere go in their favour, and Pochettino insists that prospect is his immediate priority.
"Yes, it is true that it is now time to start looking ahead at the next season, and we can now start to plan for next season," he said, "but in the Premier League you have to compete, and we will compete against Stoke.
"We want to get the three points in order to climb positions in the table and finish as high as possible.
"For the majority of my players, this was their first year in the Premier League," he added.
"It's very important for them to experience that because the Premier League is a world-class league.
"This league shows you that you always have to strive for more, and that you always have to put in a greater effort because it's very tough."