Former Queen of the South boss Johnston has endured a tough start at Rugby Park. His side have yet to win any of their four Scottish Premiership fixtures so far and the 2012 winners were knocked out of the Scottish League Cup at the first hurdle by Championship outfit Hamilton.
And to rub salt into the wounds, Johnston's predecessor Shiels said on a radio debate show after last Saturday's 2-1 defeat to Hibs that he was "surprised" by Killie's form this season.
The Northern Irishman - sacked after the Ayrshire outfit finished last season's campaign in ninth place - told BBC Radio Scotland's Sportsound show: "I am quite surprised (that Kilmarnock have had such a poor start to the season). They have got one of the biggest squads in the SPL.
"They have got 26 players. (In my time at Rugby Park, there were) not as many. If they win next week, everything will be hunky dory again. That's what happens in football. (Allan) is just in the door.
"But it's a myth that young managers are successful. They are not. I am talking about universally. They are not successful."
But 39-year-old Johnston - who still hopes to sign up "one or two" new players before Saturday night's transfer deadline - hit back by saying: "It is a big squad, there's no doubt about that. But if you look at the budget Kenny Shiels had and the budget I have at the moment, there is a massive gulf.
"I'm just trying to maximise the money I have got. We've got a lot of young players coming up from the under-20s and they are good players but maybe not quite ready to play week in, week out in the Scottish Premiership.
"So we will just need to try to bring in players that will improve the squad."
The new man confirmed he has reversed the club's ban on signing loan players which was implemented during Shiels' reign.
He said "I've brought in young Jackson Irvine from Celtic on loan. He's probably been one of our best players over the last couple of weeks.
"As long as they improve the standard of the team, I don't see what harm (loan signings) are doing. It's up to the boys that are here to prove they are good enough to play in the team."
Killie travel to Motherwell for an evening kick-off on Saturday but Johnston believes his side are nearing a winning display.
"We are capable of more," he said. "We have got good players. But it takes time. We will get there.
"Apart from the Aberdeen game, the other three league games we could easily have won so that's the positive. We need to build on these performances and stop losing poor goals. We need to improve individually and collectively."