The Blues led at half-time through Oscar's 45th minute goal but could not deny Mohamed Salah and Marco Streller late in the second half as the Swiss champions completed a smash and grab victory at Stamford Bridge.
After the loss, defender Cahill was stunned by the result but did acknowledge that Basel did perform impressively on the road.
"A big shock," he told Sky Sports of the result.
"I think we gave them a bit too much room all over the pitch.
"In the first half we were in control of the game but in the second half we didn't quite step it up that level."