Cech has made several high-profile errors with the ball at his feet in the early weeks of the new Premier League season, nearly passing the ball into his own net against Manchester City and gifting the ball to Cardiff City's Harry Arter on Sunday.
And speaking to BBC Radio 5 live, Foster insisted that Emery is not playing to Cech’s strengths by instructing him to control and distribute the ball with short passes under pressure.
"He has spent his whole career playing one style of football and now, at the end of his career, he is being asked to play another one altogether," Foster said.
"He is one of the best goalkeepers the Premier League has seen but that really is not his game."
Foster said managers had to understand the limitations of their goalkeepers and added that Watford boss Javi Gracia had allowed him to play to his strengths.
"He knows I'm OK with the ball at my feet, but I'm very good at booming it 80 yards up the pitch. He is more than happy with me doing it the way I want to do it," he said.
Cech’s shaky performances have prompted calls from Arsenal supporters to give Bernd Leno, the club’s £19 million summer signing from Bayer Leverkusen, a chance instead, but Emery is adamant that the 36-year-old is capable of adapting to his requirements.
“For me each game is progress,” he said. “Petr has experience, he is intelligent, he is doing it how we want in building up our work on the pitch.
“It is very important for me to continue doing this and improving. If you play long balls every time, you lose your personality and you lose moments on the pitch.
“We take a little risk. When you break this risk, and break through their pressing, you can find the space for attacking position.
“It is clear you can make a mistake, but we need to continue with this personality.”
Speaking in August, Cech insisted that he was relishing the opportunity to learn a new style of play so late in his career under Emery.
"I have to say that I enjoy it because I played under different managers with different styles and over most of my career I was always asked to play long, so this is a pleasant change for me," he said.
"It will be very useful when you want to beat a team who controls the game through possession.”