Taking to Instagram in the wake of the defeat, Hourihane wrote: Gutted to go out the way we did last night, really hard one to take.
"I loved my time at the club this season and wish staff players and fans all the very best moving forward.”
Earlier this month the 31-year-old admitted he would be ‘open’ to making his spell at Bramall Lane permanent, regardless of what division Sheffield United are in next season.
He said: "I’ve enjoyed my season here. I have known Hecky (Paul Heckingbottom, manager) from previous, I’m very fond of him as a person and as a manager so we’ll just wait and see.”
Hourihane, who previously worked under Heckingbottom at Barnsley, confirmed he will leave Aston Villa when his contract expires this summer.
He made 31 appearances in all competitions for Sheffield United this term and scored his first goal for the club in the 3-1 win over QPR last month.
In what could have been his final appearance for the Blades, Hourihane came off the bench against Forest to replace John Fleck in extra time.
His spot kick hit Samba’s arm before cannoning back off the crossbar.
Ollie Norwood and Morgan Gibbs-White also saw their efforts saved as Steve Cooper’s side progressed thanks to a 3-2 win on penalties.