Abbott was hoping to receive U's striker Scott Vernon as part of the deal but he turned the move down on Friday and Williams has now moved in a separate switch.
"(Colchester manager) Paul Lambert has been phoning me about Ben Williams for a while now," Abbott told his club's official website.
"We tried to do any deal that was going to be done in with a swap for Scott Vernon.
"When that fell through, Paul indicated he still wanted to take Ben and he has now come to an agreement with the player.
"We are already talking to potential replacements, and we hope to have that very soon."
Former Millwall stopper Lenny Pidgley is thought to be one of the stoppers on Abbott's radar.