The south-coast club reported the County Durham referee after taking exception to comments he allegedly made to their captain Adam Lallana in a 2-1 defeat at Everton last month.
Southampton's complaint was dismissed by the Professional Game Match Officials Ltd. (PGMOL), and the Football Association also deemed that Clattenburg had no case to answer.
Reports suggested Southampton had requested that the experienced 38-year-old official does not take charge of their matches until the matter is investigated further.
Southampton boss Pochettino feels the Premier League club were within their rights to complain about Clattenburg, but is eager to draw a line under the matter.
He said: "For me, the matter was over a long time ago as I said before. I said what I needed to after the game against Everton and we now need to look to [the] future and help referees as much as we can.
"It's time to not dwell on it; we just get over it.
"It's in the past; it's history and our main focus is to learn from it. We are fully aware that to be a referee is tough. It's a very demanding job but we also have a right to complain whenever we feel hard done by.
"And it's just up to us to try to help referees as much as we can and try and quell the situation as much as they can.
"We have to focus on the future and if we come across Mark Clattenburg again we will try and make things as easy as possible because we know it's a tough job.
"It would not be a problem if we had Mark Clattenburg refereeing for us again. We will try to help him as much as we can; we know refereeing is a very tough job that demands a lot and we will try to have a very good relationship with him and try to have a very impartial game and a fair game, which is what we all want."
The Argentine also revealed that Lallana has put the episode behind him.
He said: "The whole matter has been forgotten and it hasn't affected him at all. Adam is a very strong player mentally, so he's forgotten about it."