Despite being thoroughly outplayed in southern Spain, Leicester emerged with just a 2-1 last 16, first leg defeat, leaving the tie finely balanced ahead of the return leg on March 14.
"The Champions League is like a holiday and the most important thing is the Premier League," said Ranieri, with Leicester perilously placed just one point above the drop zone.
"If we can do something important in the Champions League then great.
"Football is great for this because the best and biggest team doesn't always win."
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On top of Vardy's first goal since December, Leicester were thankful to a stunning display from goalkeeper Kasper Schmeichel as he made a string of saves, including from Joaquin Correa's first-half penalty.
However, he was powerless to stop Pablo Sarabia and Correa putting Sevilla into a 2-0 lead before Vardy's reply 17 minutes from time.
"The first half was very, very tough," said Ranieri.
"No one wanted to receive the ball and Kasper maintained the team alive, saved the penalty, saved some shots.
"The second-half was much better, but in our good moment they scored the second goal.
"We didn't give up and scored the goal which is important for three things.
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"It gives us strength, it gets Vardy back among the goals and it opens up the tie."
However, the Italian laughed off suggestions Leicester could now be favourites to eliminate a Sevilla side that are flying high in La Liga and have won the Europa League in each of the past three seasons.
"I think we are underdogs because they are very high quality,” he said. "We will suffer in the second leg, we will try to do our best and, if we lose, it is because Sevilla make a great performance."
By contrast, Sevilla were left to rue a slew of missed chances.
"We were the better side, we had a lot of chances and we should have scored more because as it is the tie is still open," said forward Stefan Jovetic.
And Sevilla boss Jorge Sampaoli claimed he never expected the gulf between the sides to be so great despite Leicester's struggles of late.
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"It is difficult to imagine such a big difference in a Champions League game," said the Argentine. "We were dominant and we found Schmeichel in great form. If it wasn't for him, it would have been a very different story."
Yet, despite their fine form, it was a similar story for Sevilla this season as their profligacy in front of goal could come back to haunt them in three weeks' time.
"We didn't have the luck or the ruthlessness to show the difference between the sides," said Sampaoli. "We go away with a strange sensation due to their goal, but we are looking forward to the second leg and motivated to stay in Europe."
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