The Merseyside outfit have seen hopes of a top-four place diminish in recent weeks as dramatic losses to Arsenal and QPR have pushed into seventh spot, eight points behind Newcastle.
And the Uruguayan believes the last minute 2-1 loss to Arsenal at Anfield in March had big repercussions.
"The problem stems from that day," Suarez told reporters.
"It was a key match and the defeat really affected us. If we had beaten the Gunners everything could have changed.
"Our goal this season was to win trophies and qualify for the Champions League.
"The first part is fulfilled but we have failed in our other dream. Nobody could have believed we would be beaten by QPR and Wigan.
"What's gone wrong? We have incredibly missed out in the last minutes of matches, we've been affected by injuries and cards.
"The squad is angry and we really want to win at Newcastle on Sunday. Our mission is to finish in the highest position possible and to fight for the FA Cup.
"To win two cups will be the best we can give to the fans who demanded that we play in Europe's top competition.
"But there is always pressure because Liverpool is obliged to win every game and be high up in the table."
Liverpool have the opportunity to close the gap on Alan Pardew's Magpies as they travel to Sports Direct Arena on Sunday.
Newcastle could in fact boost their chances of catching Chelsea and Tottenham to secure an unlikely Champions League spot with victory against the Reds.
One of the talking points of the hotly anticipated clash will be the return of Andy Carroll to Tyneside for the first time since his £35 million pound move.
"This is going to be a special match for Andy. He needs to demonstrate his quality and I have no doubt he will,” Suarez added.
"Andy is a big forward but the pressure is not easy to overcome as a rookie. I had the same experience when I joined Ajax and Liverpool.
"Andy is working very well in training. He's always scoring and I'd be very happy if he did so on Sunday, although I don't think he will celebrate if it happens.
"It won't be easy at Newcastle. Few people thought they would be fifth [sic] and in with a chance of the Europa League but they've merited their success.
"But we want to restore our pride after our run of defeats — and we must give some joy back to the fans."
Suarez also spoke of the lengthy suspension he received earlier this season for making racist comments towards Manchester United's Patrice Evra.
"Being absent for so long was the worst period of my career because I do not like watching from the stands,” he said.
"I prefer to forget all about it — and I won't speak about Evra. My job is to score goals and I admit I have not always fulfilled it this season.
"Last year I was marked less tightly and that helped but, since August, defenders have known my style and it has been more difficult to surprise them.
"I'll keep on fighting. I want more of those big moments celebrating with the fans.
"Winning the Carling Cup was very special and now, to beat Everton and make the FA Cup final, that would be magic.
"Wembley is a temple for any footballer to play a final and to clinch a trophy is something to remember for a lifetime."
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