Leandro Cabrera scored the decisive goal in the 60th minute, heading home the opportunity created by Bryan Zaragoza's delivery to end the visitors' difficult run of results.
García was delighted with the response from his players after a difficult week, insisting that belief and togetherness had been central to the performance.
"When things are not going well, and I have experienced that myself, you have to believe. You have to trust them, bring them together, believe that your team-mate will do well and believe that you can do it too. Today we saw a great team. We were a team," he said.
"The three points are very important, especially at a ground like Villarreal's."
García had also urged the squad to put the recent disappointment behind them, including their Copa del Rey elimination, and rediscover the enjoyment of playing.
"I took them aside and said, 'Look, it has happened. Let's draw a line under it, start again, come together and enjoy ourselves.' Football is beautiful and you have to enjoy it. You can win or lose, but if you are committed to your team-mates, committed to yourself and always give everything on the pitch, you can go home feeling at peace. I think the team gave everything today."
The interim coach was particularly pleased with the contribution of the younger players, making clear that his priority was to help them progress towards the senior side.
"I want the youngsters to move forward and provide players for the first team. I could selfishly say that I don't want them to play, but no. I want them to progress, and the more who make it, the better. They cannot relax because they have it within reach. With hard work and sacrifice, things eventually happen."
He added: "They have not looked out of place at all. I actually think they have been very good. I want to congratulate them on their debuts and on the moment they are experiencing, because they have also helped the team achieve a good victory."
García also explained that his approach had been to encourage Espanyol to play with the ball rather than retreat against a technically strong opponent.
"I had a clear idea of how we needed to play against Villarreal. At times, if we had believed in ourselves even more, we could have hurt them. They are good footballers and they have to have the ball, I think. We went toe-to-toe with Villarreal in many moments. We wanted to keep possession, show personality and move forward without being afraid of the ball."
The victory offered encouragement for the incoming coach Éder Sarabia, whose preference for possession football could fit the approach García outlined.
Villarreal coach Iñigo Pérez, meanwhile, admitted his team had been left frustrated by another disappointing result. He felt his side had controlled possession and created opportunities, but lacked the precision required to turn that dominance into goals.
"We controlled the ball and generated more chances, although perhaps they were not as clear as against Elche. But when it mattered, they arrived twice, scored a goal, and we had the feeling that we could keep pushing and pushing without actually getting anywhere," he said.
"I will not use that as an excuse. I have to find the solutions because our performances are not convincing or decisive enough to produce victories."
Pérez warned against allowing frustration to take hold, particularly when opponents defend deep and make it difficult to find space.
"I don't want them to lose their bearings or move away from what they do well, because that makes things more difficult. We have to keep looking for solutions, but the coach must keep a cool head even when everything is burning around him."
The Villarreal manager also dismissed the suggestion that his midfield urgently needed a different type of organiser, arguing that the players already possessed the quality to create chances. He confirmed that it was too early to establish the extent of Gerard's injury after the defender requested an early substitution.
For Espanyol, Cabrera's goal and García's immediate impact provided a much-needed lift.