Heynckes, who coached Real Madrid to a Champions League title in 1998, told a news conference he expected a similarly strong performance from his players to the one that earned a 1-0 Bundesliga win at Mainz on Sunday.
"It makes the job harder (being a goal down) but we said from the start we are not going to give up the tie and that we'll try and make the impossible possible," the 65-year-old said. "The team will battle until they fall down."
Villarreal have the advantage for the second leg at their Madrigal stadium after Brazil striker Nilmar netted twice as a second-half substitute in Germany last week.
Defender Gonzalo Rodriguez said it will be crucial for the Spanish club to make a solid start.
"The important thing will be to stop them scoring in the opening minutes because that will give them a big lift," he told a news conference.
"But we know that we have good forwards and they will definitely get chances to score," he added. "The most important thing is that they don't create any."
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