For around 50 minutes, the Chiefs comfortably traded blows with their hosts, the game tied at 4-4. But wheels then came off in the last 10 minutes, the Lightning's triumph given some added sheen with two 59th-minute goals.
Afterwards, in his post-match interview, Zajac, struggled to contain his frustration and refused to use his team's lack of home ice as an excuse for a third straight defeat.
"For large parts of the game we had a good application, we did what we've been trying to preach to the players, we played the right way," said Zajac. "But I think at times, maybe three or four guys - especially in the third period - the effort was disgusting and you're not going to win games like that.
"And I know we're better than that and there have been some home truths said in there tonight - we just can't ship eight goals. I don't care if we're away from home every week, we can't play like that.
"It's shipping those goals that is killing us. To be honest, I think defensively, the last two games has been our strength, whereas we've maybe struggled offensively. Obviously tonight, it's just flipped on its head and it turned into a game of run-and-gun hockey and that isn't the way we want to play and it falls right into the way Milton Keynes hands.
"Player for player, there are not four goals between those two teams."
Leigh Jamieson had given the Lightning a first--period lead at 13.12 but the Chiefs were level early on after the restart when Radek Meidl scored on the power play against his former club.
The visitors then took the lead, again on the power play, when Zajac fired home, only for the Lewis Clifford's team to level matters through Rio Grinell-Parke four minutes later, Cale Tanaka then putting his team in front again at 35.35 with former GB international Russ Cowley making it 4-2 early in the third.
But the Chiefs rallied impressively, Meidl taking great delight in scoring a second power play goal against his former employers, before James Archer grabbed his second of the season at 45.16.
Clearly the next goal when it came would prove crucial, unfortunately for the Chiefs it came at their end at 52.20 on a Lightning power play, import Tomas Kana finding a way past Sam Gospel, who was beaten again just over a minute later by Calum Robertson.
With just over four minutes remaining, Gospel was then ejected on a match penalty for fighting, Miles Finney replacing him but powerless to stop 59th-minute strikes from Ari Nahri and Kana.
With work still to be completed on the team's Elland Road Rink - the first home is scheduled for Sunday, November 3 - Zajac and his players are restricted to just the one on-ice session in Blackburn every Wednesday.
But the 30-year-old said that could not be used as an excuse for his team's repeated third-period troubles.
"I'm kind of sick of hearing that as an excuse," said Zajac. "We're paid to play a game of ice hockey and if we can't be fit enough, if we can't get ourselves in shape, regardless of being on the ice only once a week, then we shouldn't be doing what we're doing, that's how I see it.
"We've got to find a way to get fitter because that's three games we've played now and we've been horrendous in the third period every game. So it is obvious to me that fitness is a massive thing and it is killing us."
Results: Sheffield Steeldogs 5 Hull Pirates 7, MK Lightning 8 Leeds Chiefs 4, Raiders 3 Telford Tigers 7, Swindon Wildcats 5 Peterborough Phantoms 0, Basingstoke Bison 4 Bracknell Bees 2.