The Oscar winner played Postlethwaite’s son in the 1993 drama, and also co-starred with him in 1992's The Last of the Mohicans.
He recalls his friend "Pos" was among his mentors - and has called on film fans to remember the 64 year old as one of the best.
Day-Lewis says, "As students, it was him we went to see on stage time and time again. It was him we wanted to be like; wild and true; lion hearted; unselfconscious, irreverent. He was on our side. He watched out for us. We loved him and followed him like happy children, never a breath away from laughter.
"He shouldn’t have gone. I wish so much that he hadn’t. There’s a tendency to make lists at this time of the year. When we get to the Best of British, if Pete isn’t at the top of that list, he shouldn’t be far from it."
Postlethwaite's The Town director and co-star Ben Affleck has also joined the growing list of friends and colleagues paying tribute to the Brit.
He says, "Pete was a wonderful actor and an extraordinary man. I will miss him as will the countless others whose lives he touched either personally or through his work. This is a great loss of a wonderful man."