An early header from diminutive Emanuele Giaccherini at St Mary's looked set to secure the Black Cats' first win of the season. However, Jose Fonte's last-gasp header secured Saints a deserved 1-1 draw.
Fonte's goal had been coming and continued their unbeaten start, but manager Pochettino said: "At the moment, I am not really happy. I am more disappointed
"I am not disappointed in the way we conceded the goal early on - I take full responsibility for that.
"That is not acceptable and it will serve as a wake-up call because it can never happen ever again. It is not right.
"At the same time I am happy and content with our industry during the second half.
"We created a host of chances and, if you look at the second half, we deserved to win the match.
"We secured a draw in the last few minutes of the game and it showed us that all the work we did after conceding that early goal was important and we fully deserved to get that goal. Perhaps even more.
"I am very clear that in the sense that we've had a very good pre-season. It shows in the effort that we put in, that we are physically strong over 90 minutes like we were last week as well."