The Socceroos midfielder came off the bench for the final 15 minutes of the match at Hampden Park and struck the post with a late effort from outside the box.
It would really have made my day had this gone in from big Tom Rogic. pic.twitter.com/bHZyATX6Yh— CelticLisboa (@CelticLisboa) April 23, 2017
It was Rogic's fourth appearance - one start and three off the bench - since returning from an ankle injury earlier this month.
Callum McGregor and Scott Sinclair scored Celtic's goals in front of 50,000 fans at the home of Scottish football in Glasgow.
Celtic will meet Aberdeen in the final in late May.
Spanish striker Jose Naranjo scored a hat-trick in the Europa League play-off Group B clash.
Another Australian gloveman - Brad Jones - also notched a clean sheet as Feyenoord remained on target for the Eredivisie title with a 2-0 win over Vitesse Arnhem.
Happy for Brad Jones and Dirk Kuyt, looks like they're gonna win the Eredivisie after Ajax got beat today.— Daniel (@DanielWy19) April 23, 2017
But Sparta Rotterdam have slumped to a fifth straight loss, going down 1-0 at home to Den Haag.
Craig Goodwin was introduced at half-time but couldn't help his side find an equaliser, while fellow Australian Kenneth Dougall was an unused substitute.
Sparta remain in the relegation zone, two points from safety with four games to go.
Meanwhile, Alex Gersbach has been forced off with injury after 17 minutes in Rosenborg's 0-0 draw with Aalesund in Norway's Eliteserien.
The Socceroos captain played a full 90 minutes in a 1-0 win over Birmingham in front of 41,000 fans at Villa Park.
Aston Villa are 12th in the Championship with two matches remaining.