The 2010 world champions qualified for the last 16 as winners of Group B ahead of Cristiano Ronaldo's Portugal, and face hosts Russia in Moscow on Sunday.
Spain are unbeaten in 23 matches, a run dating back to Euro 2016, but the Spanish federation's decision to sack Lopetegui after he accepted the Real Madrid job threatened to derail their campaign.
“It's clear that it's an unusual circumstance that doesn't happen often, but that's what happened and you have to take things as they are,” Chelsea defender Azpilicueta said in an interview with AFP. “You can't shy away, you have to accept the reality. We must do our work in the best way we can and go as far as possible.”
Fernando Hierro, the former Real captain who played 89 times for Spain, was appointed to replace Lopetegui despite limited previous coaching experience. The 50-year-old Hierro spent a single season in charge of second division Spanish outfit Oviedo, but Azpilicueta is confident he can handle the international role.
“Fernando has shown great enthusiasm, he's very involved. He had to face up to this situation and he is giving everything he has to help us, to improve the team,” he said. “I have no doubt we're going to achieve our goal.”
“The dynamic is very good, very similar to that of the last two years,” he added. “The group is united, with a desire to grow, and thirsty for victory. Each coach has their own way of working but there haven't been any big changes.”
Spain find themselves in a half of the draw that includes just one other former champion, England, although a porous defence has been a cause for concern.
Ronaldo scored a hat-trick in a thrilling 3-3 draw with Portugal in their opening game, while Spain's backline was breached twice more by Morocco.
No room for error
“It's true that we've scored goals but we've also conceded a lot of them too,” said Azpilicueta. “We're professionals, we have clear minds and we know we can offer more.
“We're an offensive team, with lots of attacking players, and we've always had this problem. When you get lots of players up front, sometimes a counter-attack can take you by surprise and lead to a chance for the opposition. We must work on this point and regain our solidity.”
Russia will have the backing of the vast majority of the 80,000 fans at the iconic Luzhniki Stadium in Moscow, and Azpilicueta is aware of the problems the home side can pose.
Spain drew 3-3 with Russia in a friendly in Saint Petersburg last November, a game in which Krasnodar forward Fedor Smolov netted twice.
“They're playing at home and it's clear we don't have any room for error,” said Azpilicueta. “We have to give our all from the first minute to the last. Russia are a solid team physically with quality players and we suffered against them in a friendly in Saint Petersburg.
“Aside from their last match, they've won with a certain ease and it will be a difficult game.”
Azpilicueta dismissed suggestions Andres Iniesta is struggling with the physical demands in Russia, in what is the 34-year-old's final World Cup. Iniesta, whose goal won the title for Spain in 2010, started each of Spain's group games but lasted the duration just once.
“Andres is a special player who can make the difference at any moment. He controls the game,” said Azpilicueta. “If we'd won our first three matches perhaps we wouldn't be talking about that. We know when not everything goes as planned people look everywhere for problems. I really have no doubt that Andres is a key player and is going to continue to be.”