Saturday's fixtures were the first round of Premier League games since the player's death was confirmed earlier this week.
The Argentinian striker's body was formally identified by an English coroner on Thursday, a day after it was recovered from underwater wreckage in the Channel.
"A lot of things were going through my mind. I knew Emiliano. I know he was looking up there. The victory and the goal is for him," said Bamba.
Before Saturday's kick-off, a minute's silence in memory of Sala was impeccably observed at Southampton's St Mary's Stadium.
But Kenneth Zohore scored a 93rd-minute winner that took Cardiff out of the relegation zone.
- 'Bags of heart' -
"It has been a tough couple of weeks," Bamba told Sky Sports.
"We knew we had to give our all today. It wasn't easy but a performance like this was very pleasing." Cardiff manager Neil Warnock was proud of his side's resilience as he paid his own post-match tribute to Sala.
"Emiliano was a fabulous lad, and it's appropriate we came down with our black armbands on and put in a performance like that," he said.
"We could easily have folded, but we were determined. We're limited, but you can't question their character and what they've got under their shirts because they've bags of heart."
Saturday's early kick-off, in a scene that will be repeated across English football this weekend, saw players from Fulham and Manchester United also wearing black armbands as a mark of respect for Sala, whose picture was displayed on the giant screen at Craven Cottage.
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