A loss to Clare on Sunday leaves Cork in sixth place in Division 2, level on three points with Derry in seventh.
Kavanagh, a part of the last Rebel side to lose to the Banner County, feels the Meath game is a must-win in order to inject confidence.
“You’d worry it might get to the stage where players are afraid to make a mistake,” he said.
“You can go out and be tentative and that nearly guarantees defeat. There is a danger of being relegated and Cork just need a win now, of any kind. The game against Meath in a fortnight is huge now.
"I don’t it’s a case of the players having to sit down and have a team meeting or anything, they all know what needs to be done.
"They just need to find something to restore some confidence because if you end up getting relegated, it’s a bad way to be going into the championship.”
The memory of that Munster semi-final loss to the Banner 20 years ago remains painful. “We trained so hard that winter,” Kavanagh said.
“It was a poor performance and it was a good Clare one too, to be fair, they still had a lot of the team that reached the All-Ireland semi-final in 1992.
"I still remember, even when the goal had gone in the ref said there was enough time but the next thing it was all over, and you had no back door then either.
“Apart from that though, Cork would always beat pretty much everyone outside the top four or five, and then those matches were the kind of ones that would go either way.
"Now, you just don’t know what’s going to happen, and you’re just left wondering where we are, we definitely seem to be outside the top 12.
“Bar maybe Kildare, I wouldnot see too many of the other Division 2 teams being in the shake-up in August, so if Cork aren’t beating them, it’s not a good sign.”
Kavanagh accepts a large turnover of players in recent times is a contributory factor, but little leeway is allowed for transitional periods.
“I saw Pa Kelly saying on the television on Sunday night a lot of players had left and it’s always going to be hard to replace that kind of leadership,” he said, “young fellas coming in will need a while to settle in.
“The thing is, the public looking in will want results, the same in the hurling, and they will get impatient if they don’t materialise.
"After the way the second round of games went, it was wide open again, and when I heard the Galway result on Sunday I was thinking it was good for Cork but then the very next one was Clare v Cork.
“All isn’t lost, if they won the rest of the games they might have a chance but that won’t be easy at all. Once you get on a slippery slope, it’s hard to get off it.”
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