Williams is the Under-23s' captain but his evening at Leigh Sports Village ended disappointingly as he was shown a second yellow card for a mistimed challenge in the closing stages.
The 18-year-old had earlier been booked after an altercation with Fulham striker Martell Taylor-Crossdale and Wood said he needs to learn from his mistake.
"He was really good [up until the sending off]," Wood told the Manchester Evening News. "He's got a red card, a one-game ban and his little retaliation, he's going to have to learn.
"He had a little flare-up with the lad (Taylor-Crossdale) earlier and got his first caution, but it's something he's going to have to learn from. He's old enough and mature enough to know he let himself down a little bit but I'm sure he'll learn from the experience."