Davies was one of Pochettino's first signings in 2014 when he was appointed as manager on a five-year contract.
The Welsh defender was playing for his country on Tuesday night in a crucial Euro 2020 qualifier against Hungary, which his side won 2-0 as news of Pochettino's sacking broke.
"I didn't really know about it obviously until after the game," Davies told reporters post-match.
"But it was a big shock, he's been amazing to work with for the last five years and it's a shame to see him go."
After initially struggling for minutes at Tottenham, Davies established himself as a regular under Pochettino with the 26-year-old making 40 appearances for the club last season.
Davies started for Wales on Tuesday as they secured their spot at Euro 2020 with victory over Hungary. Any celebrations have however now been tainted somewhat with news of Pochettino's sacking.
Former Spurs players Gary Lineker has suggested the club will struggle to find a better manager than the Argentine .
Bournemouth defender Nathan Ake was also asked for his thoughts on Pochettino's dismissal after scoring in Netherland's 5-0 win over Estonia.
"What do I think about it? It's hard to say," Ake told DAZN . "These things tend to happen at these top clubs.
"It's very unexpected because he had such a great year last season. This year not as much, but he's still a top manager."
Jose Mourinho has emerged as the favourite to replace Pochettino with sources confirming to Goal he is in advanced talks with the club.
While no deal has been struck, the former Manchester United boss is seen as a strong possibility to land the vacant position after nearly one year out of the game.
Mourinho has been without a managerial job since he was sacked at Old Trafford in December 2018.