Rovers needed to win to advance, but an early Martin Linnes strike left them with an uphill battle, and substitute Aliou Coly put a gloss on the scoreline to dump Rovers out.
Baraclough said: “I’m proud of what the players have done over the two legs. We didn’t wilt or give in.
“We could have got a couple of goals on the night, even at the end with Danny North going through on a one-one-one, but it just wasn’t our night.
“But I think we acquitted ourselves really well, over the two legs.”
Molde manager Ole Gunnar Solksjaer admitted Rovers should have had goals.
“I told Ian they should have been two or three up at half-time. We knew we were lucky not to concede two or three to be fair.
“We were better in the second half, however, and we scored a great second goal to kill the tie.”
Molde broke through for the opener inside five minutes.
Full-back Martin Linnes got the goal, stabbing the ball low past Gary Rogers after latching onto Zlatko Tripic’s pass.
Rovers’ response was hugely encouraging, as they won four corners in quick succession, after Molde centre-backs Hovland and Vegard Forren put in last-ditch blocks to deny David McMillan, Djilali and David Cawley.
Anthony Elding also had a couple of snap shots from outside the area that never really threatened, while Evan McMillan and Alan Keane put in superb sliding challenges to prevent Molde increasing their advantage on the counter-attack as the half wore on.
Solksjaer made a double change at the break, bringing on team captain Daniel Hestad and Coly, and they dominated the third quarter, with Hestad only denied a goal by a brilliant Peers block.
Baraclough sprung Cretaro and North off the bench, but Molde killed the tie with a brilliant second on 77 minutes.
Daniel Chima Chukwu flicked the ball into the path of Coly cutting in from the left, and the attacker gave Rogers no chance with a clinical finish from the edge of the box.
Rovers had a great chance to claim a consolation goal in injury-time, when the ball rebounded invitingly for North, who was left with a one-on-one opportunity, but Orjan Haskjold made a great stop, and Djilali could not direct the rebound on target.
SLIGO ROVERS: Rogers, Keane, Peers, E McMillan, Gaynor, Djilali, Ndo (Lynch 80), Cawley, Conneely, D McMillan (North 67), Elding (Cretaro 63).
MOLDE: Haskjold, Linnes, Hovland, Forren, Toivio, Tripic (Hestad ht), Ekpo, Hussain (Hoseth 78), Mostrom, Berget (Coly ht), Chima Chukwu.
Referee: D Grujic (SRB).