The Blues remain the favourites to win the Premier League after Manchester City's defeat to Liverpool yesterday afternoon.
The defeat means Manuel Pellegrini's side are now five points behind Chelsea, who have also played a game less after taking the weekend off league action to beat Spurs 2-0 at Wembley.
"It's always important to win trophies when playing for Chelsea," 24-year-old Hazard said.
"By winning this trophy, we can concentrate on the league 100 per cent.
"Before the game we didn't feel pressure or think about the Liverpool-Man City game. Of course when you see the result and that Liverpool won, it is very good for the confidence.
"The season is still long. It is not finished. Manchester City have very good players, they play very well and it will be a war until the end.
Chelsea looking to kick on after Wembley win [AMBIENT]
It's always important to win trophies when playing for Chelsea
Eden Hazard
"So it is important for us to keep going, we still have a lot of matches."
Chelsea are also still in European contention and play their last-16 Champions League second leg with Paris Saint-Germain next week at Stamford Bridge, with the tie is poised at 1-1.
"When you play for Chelsea you have to win trophies and get to the semi-final or final of the Champions League," Hazard added.
"We know it's always difficult because there are very good teams in it.
"The first game against PSG finished 1-1, it was good for us. But the tie is not finished and we need to win.
"How far can we go? I hope we can get to the final. We will see. First, we must concentrate on out next game against West Ham."
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