Emery, who has revived the Andalusian club's fortunes since replacing the sacked Michel in January, said he wanted an aggressive performance at the Sanchez Pizjuan but that it had to be controlled and targeted.
"There is a large part of the game which the heart has to play and a large part which the head has to play," he told a news conference on Tuesday.
"I don't want the players to come out with teeth bared, bite and get a red card.
"I want them to have teeth, to bite, but only what is needed to win the ball.
"They have to isolate themselves a bit from this over-excitement, which can be positive as well as negative.
"We have to remind them that their motivation has to be controlled so that it doesn't lead to a loss of balance and we can avoid shooting ourselves in the foot."
Sevilla beat Atletico 2-0 in the 2010 final to win the Cup for a fifth time, while the Madrid club have not triumphed in the competition since 1996, their ninth success.
Current coach Diego Simeone was part of that side and since taking charge midway through last season has transformed Atletico into a team capable of challenging the dominance of Barcelona and Real Madrid in La Liga.
Simeone said the key to the game in Seville would be dominance in midfield.
"Getting through to the final will be down to playing a consistent match, intense, controlling the early stages with balance," the Argentine told a news conference.
"The team that succeeds in being the strongest in the middle of the pitch will have a better chance as both sides have talented attacking players," he added.
The Cup offers Atletico and Sevilla their only realistic chance of silverware this season.
Europa League holders Atletico were knocked out of Europe's second-tier club competition last week by Russian side Rubin Kazan. Sevilla failed for qualify for Europe last term.
Atletico are in second place in La Liga, 12 points behind leaders Barca with 13 games left, and Sevilla are 12th after Saturday's 2-1 defeat at Barca.
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