The best placed rider in the day's break, Rudy Molard (Groupama-FDJ) now leads the race, with Team Sky happy another team shoulders the red jersey's burden.
"It's always mixed feelings when you lose the jersey but at the end of the day we have to look at our game plan for this race," Kwiatkowski said. "We were under control with riding the whole day, managing our effort."
"That was part of the race, that sooner or later the breakaway (was) going to put us under pressure and that's going to be difficult to control just absolutely everything.
"It was all about riding as the one unit. We were there to maintain that gap. We were not really looking if we were going to lose the jersey or not we were just riding on our own tempo which was comfortable...to stay all together to the finish line."
"it's been a hard few days for the guys and we want to save them with two and a half weeks still to go."
Sky's director Gabriel Rasch explained his team's tactics further.
"We wanted to have a breakaway that was good for us with no other GC contenders in the move. It was a super hard start but the guys did an amazing job of staying together and never panicking."
"By the end we had to let the Mollema group go, which included some strong names," Rasch said. "At the same time it's been a hard few days for the guys and we want to save them with two and a half weeks still to go. We just had to time it right against Molard to the finish.
"It's been a really good start. The guys are all in good shape and up for the fight. We have to be on it still, but I think now we can hope to have three easier days before Sunday and the really hard mountain stage."