Atletico consolidated third spot in the table courtesy of their fourth straight win as Saul and Diego Costa, the latter via the penalty spot, scored at the Wanda Metropolitano.
Saul was pleased to get on the scoresheet and called for Atletico to keep pushing ahead of Tuesday's clash with Barcelona.
"I'm very happy to have scored the opener. Scoring without our fans feels totally different, but it gave us the lead. It also generated spaces because they were defending deep and it was hard," the midfielder said.
"When we went 1-0 up, they left more spaces and allowed us to attack them in different ways. In the first half we were up against a side with six defenders and everyone else in the middle of the pitch.
"Sometimes we didn't interpret correctly what had to be done, because we tried to attack them through the middle. There was more space down the wings.
"I think we didn't play badly in the first half despite being 0-0. I think we did quite well, but it's difficult to unravel the opposition when they have six defenders and are fresh. That happens to us and to everyone else.
"We're going to enjoy this good win. I think it's the first time we won four straight games this season. We're enjoying a positive streak and have to continue like this. If we do, we'll reach our goal."
While Joselu scored a late spot-kick for Alaves, Atletico are now four points clear of fourth-placed Sevilla.
Atletico coach Diego Simeone talked up the importance of the win and is prepared for another difficult encounter at Camp Nou.
"The next game will be really tough, like every time we play in Barcelona," he said.
"Now it's time to rest and prepare, so that we arrive in the best possible shape."