Sampaoli's side have had consecutive draws with Alaves and Leganes and trail La Liga leaders Real Madrid by five points.
The defeat at Leicester, the first European knockout tie Sevilla have lost since 2012, means that their only realistic objective this season is to finish in the top three.
"I see myself lying hurt in bed feeling like a dream has gone," Sampaoli told reporters at the King Power stadium where he too was sent off after Samir Nasri's late dismissal.
"We were on top of our opponents the whole time, they sat back and we kept on probing but unfortunately we couldn't score."
Sampaoli also cast his eye back to the first leg when Sevilla dominated Leicester in such a one-sided affair that it proved to be title-winning coach Claudio Ranieri's last game in charge of the Foxes, although the Spaniards only got a 2-1 win.
"We lost the tie because we weren't capable of scoring more goals in Seville," he said.
"The two penalties we missed (Joaquin Correa in the first leg and Steven N'zonzi in the second) really hurt us. Football is often decided on the smallest details and in that aspect we were the worse team."
Captain Vicente Iborra added: "It's difficult to understand what happened. We lost after playing most of the game in their half. We shouldn't be thinking about the first leg because we lost tonight but should have scored more in Seville.
"They got one goal and they made it count."
(Reporting by Richard Martin; Editing by Ken Ferris)
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