The Blues had been without a home win since their 8-0 win over Aston Villa before Christmas.
The Spaniard told Sky Sports News: "It was very important for our supporters after four or five without winning at Stamford Bridge. Against our rivals like Arsenal, one of the best in the Premier League, it was a very good win.
"It was important to score in the first minutes and we played more relaxed. In the first half we played really well and created a lot of chances. In the second half, Arsenal have some top players.
"Today's game was important for us in different ways. We first kept going and reduced the gap to Manchester United and City. Then we played well in front of our supporters, who were very nervous."
Mata scored the first goal in today's match after just six minutes.
Chelsea remain third in the Premier League table, nine points behind the leaders.