Gylfi Sigurdsson gave Spurs an early lead, but Mata's half-time introduction helped the Blues turn the tide of the midfield battle and his free-kick enabled John Terry to head in the equaliser.
The Spaniard is still trying to erase manager Jose Mourinho's doubts over his defensive abilities, and insists he will always apply himself when called upon, whether from the bench or the start.
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"We needed to improve and we tried to, and when I came on I just tried to give my best for the team. It is what I did since I came and it is what I am going to do until the end.
"I am happy with the second half, but it wasn't enough to win.
"Last season we won here and this season we wanted to win again, it wasn't possible but the team showed that we can fight until the end."
Mata also took the opportunity to defend countryman Fernando Torres, who saw an impressive display marred with a late sending-off for clashing with Jan Vertonghen.
"I don't know [about the red card] but Fernando is not a player who goes to hurt," said Mata.
"In the first half we had some problems, in the second half we had chances to score more goals but at the end we played 10 minutes with 10 players which is very difficult against Tottenham, but we kept compact and we fought until the end to get this point.
"It was a tough game so I think a point is not bad from here, and maybe they played better the first half and we played better the second half."