Diego Simeone's Atletico secured the Liga title, ahead of Barcelona and Real, with a 1-1 draw at Camp Nou on Saturday.
Despite seeing his side finish as Spanish champions for the first time since 1996, Suarez insists the pressure will be on Real this weekend.
While Atletico have only made the final of Europe's premier club competition on one previous occasion, in 1974, Real are set to be involved in the showpiece for a 13th time.
"They are clear favourites to win; they are used to playing these type of matches. They are favourites to win just like they were in La Liga," said Suarez.
"But we've given our all and we are a team that plays with a lot of intensity, so we are going to fight to win as we always do but they are favourites to win.
"I personally don't care what people say. We are going to do what we always do and that is play football, work hard, be humble and give 100 per cent in the match.
"We'll see what happens when the match is over and who ends up celebrating."
Filipe Luis has called on Atletico's supporters to help them lift the famous trophy.
"The fans chanting is very important for us like in the final of the cup (Copa del Rey in 2013), but that was different because it was in Real Madrid's stadium," he said.
"The final in Bucharest against Athletic Bilbao (in the 2011-12 Europa League) was great because we could feel our fans chanting a lot more and that helped us and motivated us.
"I don't know how Lisbon will be, but I have no doubt that our fans will support us and will chant the whole match.
"I think that if they do as they've done in the past it will influence us positively in our match."
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