Facundo Buonanotte converted a penalty just two minutes into the second half after Aitor Areso brought down German Valera inside the box, but Iñaki Williams salvaged a point for Athletic Club with 10 minutes remaining, turning in a deflected Alex Berenguer strike to make it 1-1 at San Mamés.
Martín Anselmi felt his side's approach, built around resilience and hard work, had been fully vindicated by the result.
"Proud of my players. We were clear that we needed to compete differently, and today we showed that this is how we can be a very tough team," Anselmi said.
"We competed, coming here and competing the way we did, fighting for every ball, suffering when we had to and playing when we could, working together, which is the most important thing."
The Elche coach explained the tactical adjustments that shaped his side's approach after the break.
"I understood that at the interval we had to start pressing. We had already achieved our objective by half-time. We managed to give them less time in the second half," he said. "In the end it's an individual moment that produces the equaliser."
Edin Terzic, whose side had won their previous two matches by an aggregate of 6-1, chose to focus on the performance rather than the result.
"Once again, I like to separate the result from the performance. In the first half, the performance was a step forward. I saw a team that wanted more, and I don't think it was a step backward," Terzic said. "It's important to learn from this match and have a better performance on Wednesday."
The Athletic coach admitted his side had lost control after taking the lead in matches, and could not fully explain the second-half dip.
"It's not easy to answer. In the first half we lacked the goal, and in the second we didn't control the game like at the start," he said. "We have to see that we conceded the penalty and we were behind on the scoreboard. I think in the second half there were good moments, and I always thought we could score that goal."
Terzic also gave an update on Iñaki Williams, who appeared to pick up a knock late on.
"It's too early to know what will happen. He took a blow to the foot and we need to wait to see how it develops. I've spoken with him and he didn't give me bad feelings. It was painful at the start," Terzic said.