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The Republic of Ireland escaped with a 0-0 draw against Group B4 winners Denmark in their final Nations League match in Aarhus.
Martin O'Neill's side are now four games without a goal and this latest display will have done little to avert concerns about the team's trajectory.
Darren Randolph denied Peter Ankersen as the Danes dominated from the off.
Nicolai Jorgensen hit a post with a glorious second-half chance with Yussuf Poulsen also missing a sitter.
Feyenoord striker Jorgensen contrived to hit the woodwork from eight yards out after dispossessing Republic centre-back Richard Keogh with Poulsen blasting over the bar from six yards out with only Randolph to beat.
Other Danish chances came and went but the Republic somehow held out as manager O'Neill handed a debut to 18-year-old Southampton youngster Michael Obafemi in the second half.
The Republic's relegation to League C in the new competition was already confirmed before Monday's game, in which their poor run of form extended to only one win in 11 games.
Martin O'Neill and his assistant Roy Keane now await next month's Euro 2020 draw in Dublin
The post-match stats tell their own story as the Republic did not have a shot on target - none of their three goal attempts troubled Danish goalkeeper Frederik Ronnow.
If anything, Denmark's possession stat of 75% looked to have flattered O'Neill's side as the hosts attempted 742 passes compared to the visitors' 226.
After a torrid year for his squad, O'Neill and assistant Roy Keane will now await the draw for the Euro 2020 qualifiers, which takes place in Dublin on 2 December.
The Republic's Nations League relegation means they will drop to the pot of third seeds, which is likely to make their prospects of qualification more difficult.
O'Neill's side drew their home encounter with the Danes last month but lost home and away to Wales.
Martin O'Neill made five changes from Thursday's underwhelming goalless home draw with Northern Ireland as Keogh and Kevin Long replaced Darragh Lenihan and the injured John Egan in the defensive back three. Cyrus Christie, Aiden O'Brien and Enda Stevens came in for Glenn Whelan, Callum Robinson and the suspended James McClean.
Sheffield United's Stevens produced a couple of promising bursts down the Republic's left in the early stages as the visitors attempted to play their way out from the back instead of going long.
However, Denmark quickly gained control with Tottenham star Christian Eriksen, one of only five starters retained from Friday's win over Wales, having an effort blocked by Shane Duffy after Christie had got into a muddle on the edge of the Republic's penalty area.
O'Neill, as was the case in last month's home draw against the Danes, opted to play Christie in a central midfield role but it was asking a lot of the Fulham defender.
When the occasional Danish error did result in the Republic winning possession, the ball was inevitably quickly given back as the home team's pressing forced a hurried mistake from the Irish.
But the Republic somehow held out to half-time as Randolph maintained his brilliant form from the Northern Ireland game by saving Peter Ankersen's 40th-minute angled shot, with Seamus Coleman blocking Jorgensen's follow-up, before Eriksen fired a free-kick just over from 30 yards.
Martin O'Neill handed a first cap to Southampton youngster Michael Obafemi
Despite Eriksen's half-time departure, the Danes' domination became even more pronounced after the break as Poulsen missed a glorious chance from six yards out after Ankersen's deep cross had left Coleman outnumbered at the back post.
Middlesbrough forward Martin Braithwaite then had efforts blocked by Coleman and Duffy before Jorgensen squandered his glorious chance after Keogh's mistake.
Despite being camped in the Irish half for nearly all the remainder of the contest, the Danes could not find a way past Randolph.
Obafemi was thrown on with 10 minutes remaining but could no make impact in attack as the Republic desperately continued their rearguard action.
This was the third goalless draw in four contests between countries over the last 13 months with the other match Denmark's 5-1 World Cup play-off second leg romp in Dublin which clinched their place at the finals in Russia.
