Matsatsantsa just about secured their top-flight status, with a 14th-placed finish, ahead of Cape Town City on goal-difference.
Former head coach Gavin Hunt paid the price for the poor campaign with his dismissal in March, leaving Andre Arendse to get his team over the line with a 1-1 draw in their final league game with Golden Arrows last Thursday.
Rumours that SuperSport could be sold, renamed and relocated to Bloemfontein had been circling for the latter part of the 2024/25 campaign.
Matthews said in the Sowetan: "Two weeks ago, the rumours and speculation and all that type of stuff came out. That was tough because suddenly, from being completely together and going to the wall, there were questions from players and agents, sponsors and the technical team.
"That's been tough. Managing that has been tough; the anxiety and stress of staying in the league on its own is tough.
"But when you get constant rumours that keep coming back and never go away in terms of the club, that's unsettling. It's destabilising for human beings."
Matthews added that despite the struggles, he was proud of the way his side handled themselves during the course of the campaign.
"It's been tough for us, this group of players and this technical team. It was new and it was tough and it's been very taxing on the staff, on everybody," he said.
"We started great this season. We had a dominant draw against Cape Town City; we probably had 60-odd percent possession in that game. We felt that we played solidly, and we came out of that game, and we drew the next match as well.
"We had three draws on the spin and then we got the win against Chippa. At that point, we thought we were out. Everyone on the team was talking about preserving our top eight run.
"We knew if we had won two of our last three games against Richards Bay, [Orlando] Pirates and Stellenbosch, that we would be in the top eight."