Pochettino was heavily criticised after he made six changes to the team that won at Hull City as Saints lost 1-0 at Sunderland in the fifth round of the competition.
Morgan Schneiderlin, Jose Fonte and Jay Rodriguez all started on the bench while Artur Boruc was strangely absent from the squad altogether.
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."