Spurs were cut apart by RB Leipzig, losing 3-0 in the last-16 second leg to give the Germans a 4-0 aggregate win.
It means they have nine Premier League games left to ensure they get back in the competition next term and have work to do.
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Hit hard by injuries to key players, they are seven points behind fourth-placed Chelsea going into a pivotal game against Manchester United on Sunday.
Moura, whose workload has increased after injuries to Harry Kane, Son Heung-min and Steven Bergwijn, is confident Spurs can get the job done.
“It’s true that it’s a very difficult moment for us,” he said. “But the only way that we have is to keep fighting, keep believing.
“Now we have only the Premier League and we need to be in a better position.
“Our objective is the top four, the Champions League next season. I believe, I believe that it’s possible. We will try.
“Every season it is our objective to get into the Champions League.
“We know we need to be better. The last few results were not good and we have to improve our game. We are fighting and working hard every day and it is possible.
“We have two important games at home now and we need to win, that is it.”
It was always going to be mission impossible for Spurs to turn around their first-leg deficit with so many key players missing. Going 2-0 down inside 21 minutes did not help as Hugo Lloris was culpable for both of Marcel Sabitzer’s goals.
They had nothing in way of a response and Moura admits there is something missing in their performances as they slipped to a sixth game without a win in all competitions.
“The feeling is very bad. Everyone is very sad because we believed that we could win this game, we believed we could qualify,” he said.
“And we tried. We tried to the end, we fought, we gave everything, but it was not possible.
“We played against a very good team as well, they deserved their result, and that’s football. We need to step up now, keep our heads up now and keep fighting.
“I don’t think there is a lack of confidence. We know that we have good players, we have a good squad and we can do better.
“It is just football. Sometimes you can try everything you play well, you don’t win. It is just something that is missing. We will find the winning way again.
“What happened last season showed that we are a very good team, a very good club, that we have great players, but now is a new season, a new moment.
“I cannot tell you what happened if it is about mentality, about confidence, but we know that something is missing. We need to keep fighting and working.”