The Blues secured the victory with goals from Rogers and Garcia, leaving the Cottagers to begin the campaign without a win.
However, Arbeloa praised his players for showing character and refusing to lose their attacking ambition after falling behind early.
"We deserved a little bit more but football is not about what you deserve, it's about what you take,” the Spaniard told Premier League website.
“We have to improve in many things but this is the way we have to play, with character and ambition.
“We showed personality, they scored one goal very soon, then at the end of the first-half, the beginning of the second-half, but we were there.
“It's a new project, we as coaches don't have time but continue to play that way and we're going to win a lot of games.
“I'm really happy and proud of my players, this is how we're going to play no matter who is in-front of us."