David Bentley opened the scoring before Rovers leading scorer Roque Santa Cruz added the decisive second following a defensive mistake.
This was only the Black Cats second defeat at home in 14 League matches and they remain 15th in the Premiership.
Keane said: "We made it hard for ourselves and the second goal was a killer blow for us. Two against Blackburn is always going to be an uphill struggle.
"Danny (Higginbotham) held his hand up but he's done well since he came to us. But, you win together as a team and you lose together as a team."
Keane continued: "We got in good positions but maybe we didn't test them enough. They were soft goals and a major disappointment but they showed good spirit.
"Another five minutes on the clock and we might have got an equaliser. 2-1 and you're in with chance but overall, I thought we deserved something out of the match. We have to try and bounce back."
Keane had always warned that at no point did he expect their return to the top-flight to be an easy ride.
"Today was a big game and if we'd won that game, we would have been delighted," he said.
"No-one said it was going to be easy but we're not afraid to roll our sleeves up. We'll get ready for a battle to the end of the season."