Atrás
Rovers fell behind in the first half as goals from Emilio Lawrence and Jordan Clark gave the Hatters a two-goal advantage at the break.
However, the National League side responded strongly in the second half, creating several opportunities and putting pressure on the Luton defence.
Forest Green finished the match with 17 shots, although only two were on target, as they struggled to convert their chances.
Rovers management team member Yan Klukowski praised his side's performance despite their first-round exit.
He said: “I thought we were absolutely tremendous.
“To a man we stood up to what they had, we played some wonderful football.
“We had players today that looked like Football League footballers, Jayden Clarke in particular was absolutely sensational, a man of the match performance in my eyes.
“Probably my only criticism of the group would be that ruthlessness in the final third, shot selection, or hitting the target a bit more.
“We’re disappointed we lost the game, but delighted with the level of performance.”
Luton manager Jack Wilshere, who made seven changes to his starting line-up, acknowledged the difficulties Forest Green caused his team.
He said: “We started well and got a really good goal.
“We then had a really good opportunity to take the game to them and if you give them time to rotate and play, then they’ve got some good players.
“They put it on the sides, they’ve got quick wingers which are difficult to defend against, they put numbers in the box.”
Despite Forest Green’s attacking efforts, Luton managed to preserve their clean sheet and secure progression to the second round.