Black stepped into the breach for the 1-1 draw at Charlton barely 24 hours after Kean, who had travelled to London with the squad, suddenly announced his decision to quit.
The Scot's claim he felt he had been forced to quit prompted reports controversial club owners Venky's wanted a say in team selection.
But when asked if there had been any influence from upstairs, Kean's former assistant said: "There was none whatsoever from the owners. I named the team with the help of the coaches."
On whether he fancies taking on the role full-time, Black added: "I'll make that decision or someone else will make that decision, I'm sure. I'm sure the owners will take their time to make the right decision and I'm sure the club will go forward."
On the pitch Blackburn made a bright start to the post-Kean era, Dickson Etuhu taking advantage of some generous Charlton defending to fire them into a 16th-minute lead but the Addicks were the better side and equalised when Johnnie Jackson made amends for missing a penalty a minute earlier by diverting Danny Green's shot into the net.
Rovers goalkeeper Paul Robinson, who kept out Jackson's spot-kick with his legs, also came to his side's rescue in the second half with fine saves from Leon Cort and, in stoppage time, Bradley Wright-Phillips.
"The resilience and the attitude of the players was excellent, they made it an awful lot easier than it could have been," added Black. "There was a sombre response when Steve told them but there was a real vibe in the dressing room, it was just 'let's get on with it'."
Addicks chief Chris Powell felt his side should have taken more than a point.
"I felt the performance warranted three points," he said. "All our prep was thrown out of the window when Ricardo Fuller was taken ill before the game. But we showed good character after going a goal down and were on the front foot for most of the game."