Late goals by Scott Taggart and Alan Trouten consigned Livi to a 2-1 Premier Sports Cup defeat at the Indodrill Stadium after Bruce Anderson's opener.
Livingston had to shut down the Tony Macaroni Arena on Thursday for a four-day period following an outbreak and Martindale admitted they missed some absent players.
Martindale, whose team host Group D leaders Raith Rovers on Wednesday, told LFC Live: "For want of a better word, we have had a boot up our bum. The boys need to take it on the chin.
"I wanted to train on Sunday but I can't because of Covid, we are not allowed in the building. We will get the boys back in on Monday and we will need to do a lot, lot better than that.
"I was really pleased with how pre-season was going up until Saturday and it's a blip, but it's a blip that I will fix very quickly because I am going to be looking for a couple of players to bring into the building. Because it shows you Covid could hit at any time, track and trace could hit at any time.
"I think we have got numbers but I think we need a bit more quality in the building, and I think Saturday showed that."
Motherwell were also on the end of a quickfire double against Queen of the South as Ruari Paton struck twice just before half-time. But Graham Alexander's side came from two down to win 3-2 at Fir Park.
"We talk a lot about the mental resilience you need over the course of the season," Alexander said. "You are going to get challenged in many different ways and most of it is mental.
"It was a great response, everyone turned the dial up a bit to get back in the game.
"We are going to get more challenges during the season and we have to show that mental resilience and never give up."
Charlie Mulgrew netted a free-kick winner to earn Dundee United a 1-0 win over Arbroath and make it three wins from three for the Tannadice club.
Head coach Tam Courts told DUTV: "The pleasing thing for me is that's two clean sheets in three games, we are scoring different types of goals, and I think it's clear through different parts of the game, how it is that we want to play.
"All the credit needs to go to the players, they have been magnificent so far."
Sunday afternoon’s scheduled all-Premiership match between Dundee and Ross County was postponed with the Tayside club handed a 3-0 victory via forfeit. County have been unable to fulfil both Premier Sports Cup fixtures so far due to a covid outbreak at the club’s Dingwall base.
The Staggies also handed Forfar Athletic a 3-0 win last weekend with new boss Malky Mackay unable to muster a squad for the competition opener.