The Blues were abysmal in the first half, failing to record a shot on target, but scored three times after the break with Gallagher on target twice.
Gallagher, who apologised to Palace fans for his second strike in the 91st minute, has been praised by his head coach for his performance in south London.
Quizzed about Gallagher being compared to Chelsea legend Frank Lampard, Pochettino told the BBC: ‘I think Frank Lampard is a legend and one of the greatest midfielders in the history of football.
‘Conor is still young and still has time to achieve this level but he is doing a fantastic job for us. We are so happy with him.’
Gallagher hailed Pochettino for his tactical changes after the match and the Argentine has explained what he did to turn the game around in the second half, which included moving Malo Gusto and Ben Chilwell higher up the pitch.
‘We were flat in the first 45 minutes, very disappointing,’ Pochettino told Sky Sports. ‘We need to react to the game.
‘We need to avoid that and start a game like this so flat. Maybe there was a foul when we conceded. We started the second half really well and we scored. It was a tough game but I’m so pleased.
‘We just want to build our confidence and realise we need to be more consistent.
‘We used two strikers in between the centre back and the full back. We put Malo Gusto and Ben Chilwell higher and moved the ball quicker with Enzo Fernandez in a number 10 role. It helped us score.’