Belgium took the lead five minutes before the break through Romelu Lukaku's effort, but substitutes Oleksiy Hutsuliak and Vladyslav Vanat, as well as Bournemouth defender Illia Zabarnyi, capitalised in the second half to overturn the advantage.
"We will analyse the game, but there is no doubt that we need to improve defensively," Garcia said after the match.
"We have to play with a knife between our teeth. On Sunday we'll see if we're a great team. We have a lot of work to do, also mentally," he added.
Belgium, who were knocked out of Euro 2024 by France in the last 16 and finished third in League A Group Two with just four points from six games, face relegation from the competition's top tier for the first time since its creation in 2018.
Garcia, who replaced Domenico Tedesco in January, included Real Madrid goalkeeper Thibaut Courtois in his squad despite the player's almost two-year absence following a falling-out with his former manager.
"With a new coach, sometimes we have to find out what he wants. We made a lot of videos, we tried to train, but training is not enough in the end," the goalkeeper said.
"But we have to stay calm. We have to play a good game in front of our fans. Sometimes it's good to take a defeat like this as a wake-up call for Sunday," he added.
Ukraine travel to Belgium for the return leg on Sunday in Genk.