The Buccaneers beat Mamelodi Sundowns in a league encounter earlier in the week, and they had gone to extra time before eventually going down against Bloemfontein Celtic on penalties in their Telkom Knockout quarterfinal the previous weekend.
"It was always going to be a difficult week with three games in six days," De Sa said.
"It was really taxing and it showed up here today."
Siyabonga Sangweni pulled up with a hamstring niggle while warming up for Saturday's clash, and Ayanda Gcaba was promoted from the bench into the starting lineup in defence.
"We decided to play the same team (that faced Sundowns), but Siya's injury during the warm-up threw us a little bit off," De Sa said.
"We had to make a quick change just before the game, but we tried to play the same 11 and it was always going to be difficult."
Pirates looked flat, lacking in creativity throughout, and barring a single moment of brilliance in first-half injury time from Sifiso Myeni, they struggled up front.
"We fought hard. In the first half we were slightly better but Free State Stars sat off a bit and in the second half they had to come a little bit more at us and we were hoping to catch them in a little bit more space.
"The second half was poor, and it was more about seeing out the game and getting three points.
"As much as you tell the players to push up and play, in the back of their minds is just to see out the tough week."
Sangweni, Moeneeb Josephs, Rooi Mahamutsa, Andile Jali, Benni McCarthy and Robyn Johannes were all dealing with injuries.
"It's quite a testing time for us because we've got the whole spine (of the team) injured at the moment," De Sa said.
"Moeneeb pulled out with a shoulder injury, Siya and Rooi—both centre backs—Andile and Benni.
"So we've got five crucial players in our squad that are out and possibly long-term injuries," De Sa said.
"It's not a quick fix. They're going to need time out to get back.
"Those are the five crucial ones. Robyn Johannes is also injured still.
"There's a few that have got a couple of niggles.
"Oupa Manyisa, today we were a bit concerned with his hamstring. It was touch and go for him to play and we played him and it paid off for us.
"I hope now he can have a bit of rest and recover from that hamstring."
Meanwhile, Kaizer Chiefs beat SuperSport United 2-1 in Polokwane to retain their four-point lead at the top of the league table.
High-flying Platinum Stars defeated Wits 2-1 in Phokeng to stay in third position in the standings, while Maritzburg United edged AmaZulu 1-0 in their KwaZulu-Natal derby in Umlazi to hold on to fourth place.
University of Pretoria held strugglers Mamelodi Sundowns, still flailing at the bottom of the log, to a 1-1 draw in Pretoria.
Moroka Swallows and Chippa United had kicked off the weekend action with a 1-1 draw in Dobsonville on Friday night. – Sapa