Did Zaheer Khan's injury drive the indians in to this tough situation in the first test against England?

No. It was more the dismal batting India displayed in reply in the first innings. It was only Dravid with 102 and Abhinav Mukund with 49 that did anything of note. Even Tendulkar didn't do much with managing just 34. Zaheer Khan would have made a difference, but I doubt he would have made a substantial difference.