The Blues snapped a run of poor form with a 4-0 midweek triumph at Stamford Bridge.
"I think we deserved the win," Cucurella told the club's website. "We came from a tough moment. I think maybe against (Aston) Villa we played well, but the result wasn’t there.
"We needed a reaction in front of our fans, we started the game well, and we showed that we wanted to win and go for the three points.
"After these tough games and results, we needed to show that we wanted it from the first minute – and to the fans as well. After the four goals, you could see the intention and the desire. The intensity was there. Everyone ran a lot and we played well with each other, and I think that was the most important thing."
Cucurella was named man-of-the-match on the night and continued: "I’m very happy with my goal. It’s always important to help the team and my team-mates – we have a good connection. I think today we showed that sometimes it doesn’t matter who scores; we showed that with Levi and myself scoring because we don’t often score. The most important thing is the team.
"I always try to help the team in a lot of aspects. I’m very happy to have this Player of the Match award. Of course, the most important thing is the victory and the confidence gained – now we have 11 Premier League games left to play."
As for finding some winning momentum, Cucurella concluded: "We need to keep going this way.
"Now is the most important moment of the season. We have a lot left to play for, but we have a lot of ambition and I think we want to win all the games.
"It’s always the same in life. You have good moments and bad moments. It’s about being calm in the tough moments, keep going, and remain focused. We need to be more consistent – this is the key."