Gary Cahill scoring the opener before Mata hit a double and Daniel Sturridge a late goal as the Blues continued their blistering start to the campaign.
Mata said: "They came back very well in the 10 minutes but as a team we always believe in our qualities.
"Two goals is enough so I'm very happy today [Saturday].
"We need to keep going and keep training hard."
Cahill said: "It was a tough game and coming away from home it was a fantastic result."
The England defender was especially pleased with the way the side responded after Tottenham had hit back with two goals in seven minutes at the start of the second half to go ahead.
Of the importance of the result, Cahill added: "Just to keep the momentum going I think, we've started the season well."
The duo also welcomed the news John Terry will remain as Chelsea captain.
The former England skipper was suspended for four matches and fined £220,000 by the Football Association for racially abusing Anton Ferdinand during a Premier League game between QPR and Chelsea 12 months ago.
However, Blues chairman Bruce Buck confirmed on Saturday he had not been stripped of the armband although he had been given a club record fine.
The pair were both perfectly happy with the news of Terry.
Cahill told Sky Sports 1: "Fantastic, I didn't really expect any other outcome to be honest.
"He has been captain for many years."
Mata added: "He is a great team-mate and a really good guy."
Spurs' former Chelsea boss Andre Villas-Boas said: "It was a game full of emotion and there were lots of chances for both teams.
"We became very strong in the second half and turned things around but individual brilliance and the creativeness of Chelsea unlocked the defence and settled the game.
"We have been on a good run but now we have to bounce back.
"When you have players of this commitment, desire and ambition you have to bounce back from adversity. There are 30 more games ahead of us."
On the absence of Gareth Bale, who pulled out before kick-off after his wife went into labour, the Portuguese added: "He was missed but we have very, very good players and options.
"You saw how they behaved. (Gylfi) Sigurdsson came in and played very well. The squad is good and we have good players."