"We're disappointed," said De Sa after Pirates lost 1-0 at Orlando Stadium on Saturday, ending their slim chance of securing their third straight league crown.
"We controlled the game for most parts of the match, and we took the game to them and tried to knock it about. Today, football-wise, it wasn't bad.
"We created quite a few chances and it just didn't go our way. We can't go for first but we can go for second."
Pirates remained third in the table, seven points behind runaway leaders Kaizer Chiefs with two games remaining in their campaign.
Platinum Stars also stumbled in their title challenge, going down 1-2 to Golden Arrows at Princess Mogogo Stadium.
Three points behind Chiefs, who held a game in hand, Stars had a mathematical chance of winning the league title, but would need to score at least 10 goals in their last league clash of the season against SuperSport United to have any chance of finishing on top.
Despite their loss, De Sa believed his troops had put in an improved showing compared with their recent league outings.
"The performance today wasn't bad — the result was," he said.
"I thought we played the best we've played in at least three matches."
Sundowns coach Pitso Mosimane felt Pirates had taken control for most of the match.
"In the first half, we struggled in the midfield with three midfielders," said Mosimane.
"We couldn't get it right and they dominated, in my opinion."
Mosimane said his half-time chat with his charges had done wonders on the field.
"But then I changed it and, in the second half, we stabilised the central midfield."
While Pirates called the shots, it was a close contest, according to Mosimane.
"It was a big game between two big teams. They hit the post, we hit the post. The second half was more tactical and we sneaked in there at the end.
"At the set-pieces we benefited. Normally we suffer there, but that's how it goes."
The Brazilians moved up two spots to eighth position in the table.
"We need the points, we're desperate," Mosimane said.
"My team and supporters deserve top eight."
Elsewhere on Saturday, Maritzburg United drew 1-1 with Ajax Cape Town at Harry Gwala Stadium, Wits beat AmaZulu 3-1 at Bidvest Stadium and Bloemfontein Celtic drew 2-2 with Free State Stars in their derby clash at Free State Stadium.
SuperSport United and Moroka Swallows played to a goalless draw in Atteridgeville and Chippa United, lying second from bottom, kept up their fight against relegation with a 2-2 draw against fellow rookies University of Pretoria in Cape Town. – Sapa