Some interesting debate here. I think Cork tried to change the way they played last night, it was some of the more open, attacking, football I've seen them play, but it backfired and they conceded sloppy goals. They have a few flaws in the team that are exposed at this level, and particularly when trying to play a more open game. For all the hard work of McCormack in front of the back four he lacks quality on the ball, Brian Kerr was giving him a hard time on commentary for his distribution and it wasn't unfair. They also lacked a cutting edge up front, with lots of hard work from Cummins but little threat in front of goal. Caufield's style of play reminds me of Michael O'Neill's Rovers side to a degree. They also usually set up very conservatively in the league and in Europe, if there was one criticism O'Neill got it was that his team was fairly boring to watch, but what he had was a goal poacher in Twigg and a little more quality in midfield. Cork may have been better sticking with a more conservative and direct style against Rosenborg and taking the criticism that likely would have come had it been a dull 0-0 or a 0-1 loss, but they may have given themselves more hope in the tie.
Both Dundalk and Cork are in a strange position of being miles ahead of the rest of the league, but also having lost some quality compared to previous iterations. There's some very young players involved in both defenses, and Dundalk's was particularly badly exposed at times. With the experience gained and a couple of astute signings, both sides could still make another big breakthrough in the next season or two. You could argue that there's a 3 year cycle involved in building most teams and Cork and Dundalk are both in a second or third rebuilding phase.
Hard to see any logic in changing either manager at the moment. But, with the successes they've had, a drop from the top 2 and another disappointing season in Europe next year would probably see them gone.