Andrew Robertson conceded Scotland "didn't really show up" after their 3-1 defeat to Ukraine in Wednesday's World Cup qualifying play-off semi-final.
The tie at Hampden Park was delayed from March due to Russia's invasion of Ukraine, and it was an emotional evening for all concerned in Glasgow.
Yet Steve Clarke's team ultimately failed to match not only the visitors' intensity, but also their quality, with only some poor goalkeeping from Georgi Bushchan allowing Scotland a way back into the game.
Indeed, Scotland were fortunate not to have conceded more, with Craig Gordon pulling off fine stops early on and making five saves in total, while Artem Dovbyk spurned two golden chances to put the result beyond doubt before finally doing so in stoppage time.
While Ukraine will now switch focus to playing Wales in Cardiff on Sunday, with a place in Qatar the prize on offer, Scotland must lick their wounds before taking on Armenia in their opening Nations League game on June 8.
"Hugely disappointing. We've waited a long time for this game," Liverpool full-back Robertson told Sky Sports after another big game failed to go his way after the Reds' Champions League final defeat to Real Madrid last week.
"Our performances beforehand had been really good and to be honest we didn't really show up.
"Ukraine settled into the game a lot quicker than us and then it kind of continued really. We knew they were probably going to get tired and that was the case but we gave ourselves too much of an uphill battle.
"We didn't play the way we wanted to play, that's the most disappointing thing. It's passed us by now. After a positive campaign, we've let ourselves down.
"We have to hurt, have to reflect, tomorrow's a new day. We've got the Nations League, we have to try and push.
"That's the World Cup gone for us for another four years, that's really hard for us because we all have dreams of trying to play in that big tournament and we didn't put in a performance that justified that."
Scotland were unbeaten in 12 home games at Hampden Park coming into this match (W8 D4), meaning Ukraine have ended their longest unbeaten run on home soil since the 1970s, when they went 16 such matches without defeat.
"We have to stick together, we know there'll be scrutiny coming our way and we know we'll be under fire, but inside we have to stick together," Robertson added.
"As a group we've made massive strides in a couple of years, there'll be a time to take perspective of that, but tonight's not that night. We have to dust ourselves down, go again."
Scotland have failed to qualify for any of the last six World Cup tournaments since appearing at the 1998 edition. Between 1974 and 1998 they missed only one of seven tournaments.