After going ahead inside three minutes courtesy of Morgan Schneiderlin's well-taken opener, Saints were pegged back and the hosts went in ahead at the break.
Rickie Lambert's 100th goal for the Club levelled matters soon after the restart, but a debatable penalty decision and unfortunate own-goal ensured the points went the way of the hosts.
"I don't think Newcastle really deserved to win the game but that's how it happened," Pochettino told Saints Player
at full time.
"We have to divide the game in two halves. In the first half we got on the scoresheet really quickly but from then on we struggled to manage the game.
"We weren't able to keep it going because Newcastle were pushing us well, although we did make some mistakes - particularly for their first goal.
"It was a very tough half, but we equalised in the second half with a very good goal.
"We were doing really well when we were pressing on to win the match but we conceded the penalty. After that, the fourth goal was really unfortunate."
The manager felt his players suffered from a number of moments of bad fortune during the course of the game.
And he was particularly aggrieved with the build-up to Papiss Cisse's stunning goal to put Newcastle ahead just before the break.
He insisted: "We've reviewed the second goal and there was a clear foul on Clyney (Nathaniel Clyne), and that was followed up by a clear offside.
"Despite that, we managed to make it two-all and the team was playing well until we conceded a penalty from Danny Fox's completely involuntary handling of the ball."
There had been cause for concern shortly before Newcastle's third goal, when the injured Luke Shaw had needed to be replaced by Fox.
But Pochettino said the substitution was purely precautionary and that young left-back Shaw should be fine for next Saturday's visit of Queens Park Rangers.
"[Shaw] had a knock on one of his thighs," the manager confirmed at full time.
"We're more-or-less certain that it's not a big thing and he'll be able to play next weekend."
Preparation for next week's game against the table-proppers will begin quickly, with Pochettino insisting the squad have reason to remain positive despite today's set-back.
"I've told the players to keep their chins up and to think about the next game," he said. "We can't change the result of this game.
"We have to analyse what we didn't do well today and make sure that doesn't happen again so we can prepare for our next game at St Mary's as best we can."