The Blues made a strong start and benefited from an early goal, which Alonso believes gave his players confidence.
Chelsea created further opportunities before the Cottagers found a way back into the game, but the visitors remained composed and continued to compete without the ball.
“We have managed to suffer, to complete and do whatever it takes in certain moments and that is why these three points feel great,” Alonso told Premier League website.
“The early goal helped to give us confidence. We had chances to score a second one before their equaliser but we were stable and comfortable even without the ball.
“The three strikers combined well to create chances. To win games away you have to roll up your sleeves and fight to defend your goal. I think it is a good first day for us.”