The 22-year-old did not start the Championship encounter against Rotherham United at the City Ground, but he came on as a substitute in the 79th minute.
Barrow was delighted to have made his first appearance for the Reds following his loan move from Swansea last week.
Forest produced a good display against Rotherham and ran out 2-0 winners to maintain their challenge for a top-six finish in the Championship this season.
Dougie Freedman’s side had 48% of the possession, 14 shots of which two were on target, and five corners.
Barrow himself did well in the few minutes he was on the pitch, ending up with a pass accuracy of 86% and winning one of the two dribbles he had tried.
Forest are currently ninth in the Championship table with 57 points from 38 matches, eight points behind sixth-placed Brentford.