Victory for Spurs saw them again close the gap to leaders Chelsea at the top of the table to four points ahead of facing rivals Arsenal on Sunday.
Tottenham have a tough run-in, starting against Arsene Wenger's men, but Pochettino is happy that his side are still alive and kicking in the title race after Christian Eriksen's decisive late goal at Selhurst Park.
"It was unbelievable - a very good performance," he told Sky Sports. "I think [in the] second half we played much better than in the first half.
"It was difficult in the first half for us to move the ball and find the space, but we changed the shape at half-time and it was more fluid - we started to find the space and started to push Palace deeper and deeper.
"It was good to get the three points and be alive in the race for the title. The challenge is to keep going.
"It is always better to win, but it is true [the Arsenal game] is a big derby, perhaps the last at White Hart Lane, and I think it will be an exciting game."
"Wow. It was an outstanding team effort by the players, who have had less time to recover against an exceptionally good side," Allardyce said.
"Our application was outstanding and we gave Tottenham a hell of a game in the first half, nip and tuck, but of course it would happen that we would tire given the lack of recovery time compared to Tottenham.
"It was a terrific goal by Eriksen, but a shame for the lads they could not hold out."