Chelsea have won eight of their last 10 matches in the top flight, but a slow start to the season means that the Blues still remain 14 points adrift of leaders Manchester City in the standings.
Alonso has admitted that he has been pleased with his side's response, but the Spaniard says that the club cannot afford to drop any more points.
The 26-year-old told the club's official website: "We have to do what is in our hands and win our games. It was very disappointing the defeat against West Ham but the response this week was good and this is the way to follow in our next few games.
"Big teams have to do this and we did it this week. It is still a long way to go and we have to win every game now."
On Saturday, Alonso scored the only goal of the game as Chelsea recorded a 1-0 win against Southampton at Stamford Bridge.