Pochettino was heavily criticised after he made six changes to the team that lost 1-0 at Sunderland in the fifth round of the competition.
But the Saints boss insisted he had picked the best side available to him, and said he felt that some of the comments in the aftermath of the result had been disrespectful to his players.
He said: “During the time we’ve been here we’ve always shown proof that we fully care about the English competitions, especially the FA Cup and the Capital One Cup, and we’ve always shown that full respect towards those competitions.
“It is true that day we did have a bad day. Perhaps we were not as fresh as we could have been and I completely understand the disappointment of the fans, because we were also disappointed in the same manner and to the same extent.”
Pochettino added: “As we always do, we chose the best starting eleven, what we thought was the best starting eleven for the club, for the team, that day.
“We made the correct decision in picking those players, but it is true that we didn’t actually get through the tie. We weren’t able to do that on that day, and it’s not because of a lack of respect.
“That’s never the case, because we fully respect the FA Cup.
“It is true that we had had two tough games before that, here at St Mary’s against Stoke and then a long trip away against Hull, and perhaps the team was strained mentally and physically, that is true.
“Perhaps the team was not as fresh as it could have been, but the players that we chose were the best players for that day.
“It’s also clear that the third game is always the toughest out of the three, and it’s clear that we didn’t have a good day.
“But I completely reject any sort of criticism that we didn’t put out the best team for that day.
“We’ve shown in the time that we’ve been here that we’ve always picked the squad that’s best for every single game and we’ve also shown that all players can play, and that all players have the capacity, have the skill, to play in the Premier League, and those players were no different that day.
“I also want to say that, not exactly that it makes me angry, but more than anything it makes me sad, the fact that with these type of comments that came after that game, they’re quite disrespectful to the players that were actually on the pitch.
“I think all players that are part of this team are full professionals, they will have the capacity to play in the Premier League and in the FA Cup, and I think the comments that came after that game were very disrespectful to the players that were on the pitch that day.”