Liverpool conceded in injury time in losing to Villarreal 1-0 in the first leg of the Europa League semifinals on Thursday.
The match looked set for a draw until the second minute of added time, when Adrian Lopez scored for the host after a quick counterattack.
In Ukraine, striker Kevin Gameiro converted an 82nd-minute penalty for two-time defending champion Sevilla to draw away with Shakhtar Donetsk 2-2.
Liverpool seemed set to return home with the scoreless draw until midfielder Denis Suarez broke into the area and passed inside to an unmarked Lopez to tap in. Liverpool players complained of offside but video replays showed Lopez appeared to be in a legal position.
"We can do better defending than that but we look for positives now," Liverpool defender Kolo Toure said. "There is another game, we had chances to score. We know we can do it, we just need to believe. We just need to learn from the mistakes, and play the same game we did against (Borussia) Dortmund (in the quarterfinals)."
The result ended Liverpool's seven-game unbeaten streak. The English team hadn't lost in 12 games in this season's Europa League, a record that Villarreal matched with its win on Thursday.
"We're going to throw the kitchen sink at them in the second leg," Liverpool coach Juergen Klopp said. "There's no shame in going out in the semifinals but if you are going to go out in the semis, then do so kicking and screaming."
Villarreal has won all seven of its home games in this season's competition, conceding only once.
"We played a good game," Liverpool goalkeeper Simon Mignolet said. "Everyone saw Villarreal's quality but we had some chances to score. It was a very tactical game. They were tough to break down but with the fans behind us it is there to play for at home (next week)."
Mignolet made a great save in the 87th on a shot by Cedric Bakambu, but in stoppage time he committed to Suarez, who calmly set up Lopez perfectly.
The Europa League gives Liverpool its only chance of winning a title this season, the first for coach Klopp in charge. It also can give the English team a chance to return to the Champions League if it wins the title.
The second leg is next Thursday in Liverpool.
In Ukraine, Victor "Vitolo" Machin put Sevilla ahead in the sixth minute by clearing a defender inside the area before sending a low shot into the net.
Midfielder Marlos broke through the Sevilla defense in a breakaway to equalize, then made the cross for Taras Stepanenko's 2-1 goal with a firm header in the 36th.
Gameiro's tying score came from the penalty spot after Mariano Ferreira fouled Vitolo with a late tackle. The striker missed a few good chances just minutes before converting from the spot.
Sevilla's Michael Krohn-Dehli was carried off in the 73rd , less than 15 minutes after he went in, with what appeared to be a serious knee injury.
Shakhtar played its home game in Lviv in western Ukraine because of the longstanding conflict with pro-Russian separatists in Donetsk.