Cole, who made his senior England debut this week against Spain after 10 goals for his club this season, limped off after 34 minutes at Upton Park.
"We don't know how bad it is yet," said Zola. "He is going to have an X-ray in the next 24 hours and hopefully it will be just a twist."
Zola also lost Luis Boa Morte to a hamstring tear and the winger was jeered off by his own supporters when he was replaced just after the break when his side were behind to Stewart Downing's opener.
"As soon as he makes a mistake they pick on him and he doesn't deserve that," Zola said.
Downing's opener came in the 22nd minute, a header from Gary O'Neil's cross after Matthew Upson and James Collins failed to clear.
David Di Michele and Diego Tristan were guilty of missing chances but the hosts eventually drew level.
Savio Nsereko was thrown on by Zola and his free-kick was headed in by Herita Ilunga.
"We had so many chances that I was afraid we weren't going to score," Zola said.
"We didn't deserve to lose and a draw may have been fair. A replay is not great news but we want to go through. It will be tougher but we want to go through."