Skipper Scott Brown is confident there will be a positive reaction after Celtic lost their lead to Rangers at the top of the Ladbrokes Premiership on Sunday.
Hoops attacker Ryan Christie saw red in the first half for a reckless challenge on Livingston's Scott Robinson at the Tony Macaroni arena before the Livi midfielder fired the West Lothian side ahead two minutes after the restart.
Striker Lyndon Dykes doubled that lead in the 73rd minute for the Lions' first-ever win over the champions who lost their first league match of the season.
Rangers' 5-0 home win over Hamilton later in the day took them two points clear of their Old Firm rivals after eight games and going into the international break.
Brown said: "It's disappointing, especially going into the international break when you have a couple of weeks until your next game.
"But sometimes it's good for you as well.
"We've lost the lead during the season before and we've managed to bounce back.
"This team has that grit and willingness to win games we probably shouldn't. It wasn't our day, we didn't perform as well.
"But it's a long season and we know we can do better."
Livi boss Gary Holt insists Dykes, born and raised in Australia and who moved to Scotland in 2016 when he joined Queen of the South, could step up the international stage with Scotland.
Both Dykes's parents are Scottish, which came as surprise to Holt.
He said: "I was championing Lyndon for Australia until Sunday morning when I found out he was eligible for Scotland.
"I think he can step up no problem.
"He has shown his qualities and it is refreshing to see that he doesn't care who he is playing against, he could be playing with his pals or live on television, it doesn't matter.
"I told him to keep working hard, keep your head down and you will get noticed and get your opportunity."