Jay Rodriguez gave Saints - who tried to exploit some uncharacteristic nervousness in home ranks - an early lead, but Wayne Rooney's double ensured United won 2-1 at Old Trafford, despite an impressive second-half showing from the visitors.
"We did notice that," Pochettino said.
"In the second half we were dominating the game and taking the game to them.
"We were just a bit unlucky in front of goal. We should have scored at least one.
"But, especially going forward, the way we played in the second half was the way we want to continue playing."