Alberto Zaccheroni's men need to beat Colombia on Tuesday, and have results fall their way, if they are to qualify out of Group C, but they have produced just one goal in 180 minutes at the tournament.
Nagatomo called on his team-mates to believe they can break down the Colombian defence, which has shipped just one goal so far.
"We still have one match left to play and there is also possibility to get through. All we have to do is to just believe and achieve it. We will believe and play," the Inter man said.
"Firstly we need to adjust our mental conditions rather than physical conditions because we cannot go into the next game without it, so we just have to be positive and move on.
"If we had scored when we created several opportunities against both Ivory Coast and Greece, everything would have changed.
"But we are in the current situation just because we could not finish those chances.
"If we do not miss the scoring opportunities, we have the chance to win, so I'll believe and play."
Nagatomo said Japan had been lacking creativity with their crosses so far in Brazil.
The Japanese have just one point from their first two matches in Group C but remain alive to qualify for the last 16 should they beat Colombia by two goals and Ivory Coast fail to defeat Greece, or simply win and hope the Greeks edge the Ivorians in a low-scoring affair.
However, Japan have only Keisuke Honda's goal to their name so far, while Colombia have produced five, and Inter full-back Nagatomo said they must be inventive on the wings if they are to down their South American opponents in Cuiaba.
"It is about the quality and creativity of the crosses as we need to think where we should deliver into more spacious areas," Nagatomo said.
"We have persisted to deliver crosses as our strong point even against physically strong opponents like Australia.
"Actually (Shinji) Okazaki and I created many chances and I delivered a cross for a winning goal in the (Asian Cup) final against them.
"But we still need more creativity as there is no space when the opponents stay at the back, so the key to solve the problem depends on creativity.
"If we can make better quality of crosses, passes and shots in the last moments, we will be able to score against any opponents.
"So I will think over the quality of those things and make the best of it in the next game against Colombia."