The centre-back faces a one-match ban, to be served when Town face Championship rivals and leaders Nottingham Forest in the second round of the Capital One Cup back at the John Smith’s Stadium tomorrow.
Former Falkirk man Wallace was sent off for the first time in his career in first-half stoppage time for a professional foul on Igor Vetokele, who was to score the Londoners’ last-gasp leveller after Nahki Well’s 50th-minute goal for Town.
But Town argued the goalscoring opportunity wasn’t obvious, because there was a covering defender in Joel Lynch.
“We’ll certainly look to appeal, because we don’t think Murray was the last man,” said Lillis, who was taking charge for the fourth time and the first at home since the 4-0 opening-day mauling by Bournemouth which led to Mark Robins’ departure.
“It made it hard, and we had to regroup at half-time, but I was pleased with the way we went about the second half.”
LIllis also thought Town should have had a late penalty when returning striker James Vaughan went down under Tal Ben Haim’s tackle.
“I think if that tackle had taken place anywhere else on the pitch it would have been a free-kick,” said Lillis.
“Vaughany was about to shoot, there was no need for him to go down.
“The referee said he was close to it, but I think there are a couple of decisions he needs to look at.
“Managers and players make mistakes, and so can referees.
“But we can’t change the decisions. They’ve gone now.
“Not getting all three points hurts, but at least we got one.”
Lillis will run checks on ankle injury victims Wells and Lynch, Lee Peltier, who was forced off with a recurrence of his groin problem, and Jonathan Hogg, who missed out because of a calf strain.
Town have lost just one of his four games at the helm, and he goes for a third win tomorrow.
Former Charlton chief Chris Powell continues to be linked to the vacant managerial position.
But academy manager Lillis says he is happy to continue for as long as required.
“I will just keep going until the chairman makes his decision, whether it’s tomorrow or in two months,” he said.
“My focus is on keeping the football side of things running smoothly, and I am enjoying that challenge.”