The feeling is inspired by their efforts against Real Madrid last weekend and Vazquez believes his team are now capable of ending their losing run.
In what was Vazquez's second match in charge since being appointed as successor to Domingos Paciencia, Deportivo suffered their sixth straight defeat as Real emerged from the contest at the Riazor on Saturday with a 2-1 win.
The visitors only secured the three points through goals from Kaka in the 73rd minute and Gonzalo Higuain in the 88th, though, having fallen behind to Riki's 35th-minute strike.
Although it was ultimately another loss, Vazquez regards Deportivo's overall display on that occasion as a success.
And with the Galician outfit - currently nine points from safety - still having 13 games to save themselves, the 58-year-old is certainly not about to give up on their chances of beating the drop.
Speaking ahead of the home encounter with eighth-placed Rayo, Vazquez said: "Although we lost the points against Real, with the way we played, for me, it was a win.
"The 'can do' attitude is to never give up, to see that you are not relegated until the mathematics tell you no more, and to be a winning team.
"Even this is not our last chance, because there would still be time to get seven or eight wins.
"When we get the first win, the second will be easier. Once you are winning, everything seems easier. And now we have a great opportunity to get a win."
Rayo striker Leo Baptistao is himself eager to return to winning ways after the team's recent back-to-back defeats to Real Madrid and Real Valladolid, but he expects Depor to provide a tough test.
"We face every game always looking to win. We've lost two straight games and we will not relax," the Brazilian said.
"Deportivo will be very dangerous opponents because they need to win.
"They will come out very strong, so we have to go 100% from the beginning of the game."