Steve Davies scored in injury time at the Crown Oil Arena to earn the League One strugglers a fifth-round replay against the Premier League high-flyers.
"The FA Cup is magic. We have another opportunity at Wembley, the same situation like before," Pochettino told BBC Sport after the game.
"I was so calm on the bench because I know very well what happens if you believe the tie is over. That happens. We concede two clear chances, one was nearly and one was a goal."
"I was not surprised [by how Dale performed]. This competition is completely differently. Newport gave us a fantastic game [in the previous round] and they lost their next game in the league 5-0.
"The motivation is always massive. It's not easy to play this type of game. Of course we wanted to win but we have the possibly to win.
"We have all the squad fit and it will be another game to provide players with the chance to compete on Wembley and we have the possibility to reach the quarter finals."
Tottenham resume their efforts to finish in the Premier League's top four when they face Crystal Palace at Selhurst Park on February 26.