Ireland are now depending on other results going in their favour to remain in the competition. Should France beat Spain this evening and Switzerland on Saturday, coupled with an Ireland win over Spain, progression would come down to goal difference.
Conor Hourihane (Sunderland) and Richie Towell (Celtic) were selected in the Irish starting line-up after missing Sunday's group opener against France due to suspension and illness respectively.
Ireland captain Conor Clifford came through a fitness test today and looked sharp in the midfield area.
However, Ireland were dealt a blow with only nine minutes gone when Gearoid Morrissey had to be substituted with an injury. Paul Murphy, who scored the goal against France in Sunday's 2-1 defeat, replaced the midfielder.
The Ipswich Town attacker was close to making an instant impact a minute later when he latched onto a free-kick but the Swiss defence cleared the danger.
Switzerland then created two good openings, Steven Ukoh volleying over on 14 minutes and Dino Rebronja cleared Ger Hanley's crossbar with a shot three minutes later following a slick counter-attack.
The only goal of the game arrived nine minutes into the second half. Steven Ukoh's free-kick into the box caused confusion and the ball sliced off the unfortunate Gavin Gunning and into the net to leave Irish goalkeeper Ger Hanley helpless.
The Swiss grew in confidence after finding the breakthrough and Hanley had to be his best to deny Fabio Daprela's crisp shot on 57 mins.
Fresh legs were needed for Ireland and Robert Brady was introduced for Conor Hourihane on the hour mark to inject some pace in the attack.
Paul Murphy led the assault on the Switzerland goal in the final ten minutes by hitting a screamer from 20 yards which goalkeeper Rene Borkovic did well to tip over the bar.
Ireland pushed forward in numbers for the last couple of minutes searching for the equaliser and Greg Cunningham asked questions of the opposing defense with an inviting cross that had to be scrambled away for a corner.
From the resulting delivery, Aaron Doran found Robert Brady in space but the Manchester United youngster headed wide.
In the dying moments of stoppage time, Switzerland's resolute defence was breached again only for Irish substitute Darragh Satelle to prod his shot over the crossbar from six yards out.
McCaffrey said afterwards: "We need a miracle now to qualify. We're relying on France to win their last two games."
"I'm disappointed for the boys because they've worked very hard this week and kept their discipline."
"We retained possession better as the game wore on but Switzerland were very well organised. Overall, they defended brilliantly."
He added: "If we do lack anything in this squad, it's a natural goal-scorer. Having said that, there are a lot of quality players in the group and I'm certain that a fair amount of them will progress to the Under-19 International team next season."
REPUBLIC OF IRELAND: Ger Hanley (Salthill Devon), Padraic Ormsby (Crumlin United), Danny Joyce (Belvedere), Mark Connolly (Wolverhampton Wanderers), Gavin Gunning (Blackburn Rovers), Conor Clifford (Chelsea), Gearoid Morrissey (Ringmahon Rangers), Aaron Doran (Blackburn Rovers), Richie Towell (Celtic), Conor Hourihane (Sunderland), Greg Cunningham(Manchester City)
Subs: Paul Murphy (Ipswich Town) for Morrissey (9 mins), Robert Brady (Manchester United) for Hourihane (61 mins), Darragh Satelle (Hull City) for Cunningham (78 mins).
Subs not used: John Sullivan (Crumlin United), John Dunleavy (Wolves), Gavin Carlin (West Bromwich Albion), Shaun Timmons (Birmingham City)
SWITZERLAND: Rene Borkovic, Bigambo Rochat, Fabio Daprela, Philippe Koch, Michael Lang, Steven Ukoh, David Frey, Taulant Xhaka, Admir Mehmedi, Alexandre Pasche, Dino Rebronja.
Subs: Patrick Durig for Rebronja (78 mins) and Xherdan Shaqiri for Pasche (80 mins).
Subs not used: Nassim Ben Khalifa, Hrvoje Bukovski, Fisnik Sabedini, Stefano Milani, Sven Lehmann.
REFEREE: Libor Kovarik (Czech Republic).