Julian Alvarez had Atletico ahead at halftime after a successful penalty before Kylian Mbappe struck just after the break.
Vazquez said afterwards: “It's a point that's not enough for us. We have set out our game plan and where they’ve taken the lead without having done practically anything. After that, the team shows character and continues attacking. After the break, the team came out really energised, then we got level and in the end, we had several chances to make it 2-1 but it didn't come.
“We pushed a lot in the second half, we created lots of chances with patience, good crosses and final balls, but we lacked a little luck to score the second goal.”
On being top of the LaLiga table, Vazquez said: “That’s the positive side, that we continue to be leaders. We’re where we want and should be, and we’re going to fight until the end.
“The reception has been incredible. We felt on the bus how they pushed us and then when we equalised, the atmosphere in the stadium was tremendous. The fans are part of the team and will help us win titles.”