Trailing 2-0 at halfime, Chelsea fought back to win 3-2 with Cucurella levelling on 70 minutes before Enzo Fernandez struck an injury-time winner.
"We are very happy," said Cucurella at the final whistle. "We work for moments like this. We showed the mentality of the team.
"We went 2-0 down at half-time and there were doubts and probably not too many people believed in us. Then we speak during the half-time, we go with a lot of energy and we come back, so we are very happy.
"Sometimes when you are losing you lose confidence, but in both games we stayed in the game, we did things right and we have a lot of quality, so if we stick together and we fight together these things can happen."
Cucurella also said: "It was difficult. West Ham played a really good first half as well, so we have to give credit to them.
"All together we want the same end to the game, which is to get the three points, and we are really happy. After being 2-0 down at half-time we showed our mentality to play a really good second half. We stick together in tough moments and we deserved this win.
"In the end we are a team. I think we have a very strong squad, we have a lot of talent, and today we showed that.
"Now we have three more points and we have to continue in this way because at the end of the season all of us will have our moment, our opportunity, so we need to stay together."