Delaney told Virgin Media Sport that the results need to turn now for Kenny if he is to hang on to his job in 2023.
Kenny's side turned in an impressive first half performance as they stormed into a lead at Hampden Park, but the home side roared back in the second and seal a 2-1 win with a late penalty.
The result leaves Ireland facing the threat of relegation to the third tier of the UEFA Nations League if they lose against Armenia in Dublin on Tuesday night and former Ireland defender Delaney told Virgin Media Sport that the results need to turn now for Kenny if he is to hang on to his job in 2023.
"It was an okay performance, but the reality is we are preparing for a relegation or wooden spoon game against Armenia,” said Delaney, as he backed up his comments made in an exclusive interview with the Sunday World last weekend.
"We have to win that game and then we can pick the bones out of the campaign overall.
"He’s two years in the job and look at his track record. Lost the play-off, finish second bottom in his first Nations League, out of the Euros very early and now second bottom in the Nations League. Put it all out there and it's not a good issue.
"How long does this go on for? How long do you keep saying we are going somewhere.
"He will be judged on the next Euro campaign. If we are out after two games and we are still talking about this, then I think a line needs to be drawn.”
Ireland legend Liam Brady described Ireland’s performance as “very encouraging” despite the defeat.
"Going forward, I’m happy,” declared Brady. "A lot of these kids are maturing and if Troy Parrott takes his chance in that match, things are very different.
"The table doesn’t read well as we only have four points, but going forward into the Euros, this is a team that’s going to get better.
"It was a great game to watch. Both teams got stuck into each other and I enjoyed it.
"I would forget about the fact we lost this match and look forward to next March and the Euro qualifiers.
"We have had some poor games under Stephen, but I think we are going in the right direction.
"I had my doubts whether we should give him a new contract, but it feels like the team is growing under Kenny and I’m encouraged by what I saw, even if the table doesn't ready well.
"Let’s hope we finish this Nations League campaign with a resounding win on Tuesday night Lansdowne Road.”