Clattenburg said he allowed Spurs to "self-destruct" in their 2-2 draw with Chelsea so that he could not be blamed for Leicester securing the Premier League title.
On Tuesday, Pochettino was unwilling to talk specifically about Clattenburg's remarks, instead being keen to stress how difficult a job referee's face.
When asked about Clattenburg, Pochettino said: "No comment."
When pushed further, he said: "Two years ago, no comment. Sorry I'm not going to say anything."
Asked later in the press conference about whether referees should speak about the matches they have officiated on, the Argentine said: "I don't know. It's so difficult to talk about that subject.
"My position now is I want to be away and I don't want to talk about the decision of the referee. I don't want to talk about their behaviour. I don't want to talk about if they were good or no good.
"I understand that it's so difficult. It's not easy to be a referee. We can see in every single training session when I'm in the middle of two groups when they are competing it's so tough to say 'foul, no foul', 'handball, no handball', 'penalty, no penalty' or 'it wasn't a red card, it's a yellow card'.
"We are the first to know their job is so difficult but I think I try to help them. It's better to stay quiet and say nothing because I'm not going to help if I say some comments. I prefer to stay quiet and what happens, happens, describe the situation and never argue again about whether it was or wasn't, or right or wrong.
"I prefer to be quiet and be focused in trying to help my team because if not, then we are going to distract the focus and today my focus is to try to fix the problem that we have in the team which is winning games.
"We need to be 100 per cent focused on winning, help the players in being better and to improve, and that is what we are going to do."