Mick McCarthy’s men went into the game at the Aviva Stadium in Dublin knowing a win would see them leapfrog their opponents and book their spot at EURO 2020, but Martin Braithwaite’s second half opener left them with a mountain to climb.
Ireland fought back, though, and finally levelled five minutes from time when Matt Doherty’s first international goal brought them level.
They needed just one more to secure qualification, but Denmark held on to seal second place in Group D.
Clark – who has netted in both of his last two outings for Newcastle United – appeared as a half-time substitute for John Egan, winning his 33rd cap for his country.
Elsewhere in Group D, Fabian Schär’s Switzerland pipped Denmark to top spot with a 6-1 victory over Gibraltar.
The United centre half missed out on the win, though, as he remained on Tyneside to work towards full fitness following a knee injury.
Slovakia’s hopes of qualifying remain in the balance after their 3-1 defeat to Croatia, in which goalkeeper Martin Dúbravka was booked.
Dúbravka’s side must now win their final Group E game and hope that fellow contenders Wales and Hungary draw in their fixture to keep their qualification hopes alive.
Emil Krafth’s Sweden will definitely be in action at EURO 2020 next summer, though the defender missed out on featuring for his country during this round of fixtures as he became a father for the first time.
Young midfielder Joe White collected another cap for England Under-18s on Monday, as they beat the Czech Republic 1-0 in a friendly at the Pinatar Arena in Spain.
White made his debut for his country in the 5-2 win over Russia last week, before making a substitute appearance in the 4-4 draw with Norway over the weekend.
And Oisín McEntee skippered Ireland Under-19s to a 13-0 win over Gibraltar on Saturday, playing the opening 45 minutes, while Matty Longstaff will hope to again feature for England Under-20s in their friendly against Iceland in Wycombe on Tuesday night.
Miguel Almirón and DeAndre Yedlin also could be in action for Paraguay (in a friendly against Saudi Arabia) and the USA (in a CONCACAF Nations League clash with Cuba) on Tuesday.
