Costa Rica claimed a surprise 1-0 victory in Group E at the Ahmad bin Ali Stadium, putting a huge dent in Japan's hopes of reaching the last 16.
"I need to value and appreciate what my players have done to get this result," Suarez told a news conference.
"We had to face many challenges. However, we firmly believed and wanted to do things well to be 100% committed to our country to play well against an opponent such as Japan.
"Yes, we won against Japan, but we must emphasise that we won against this (particular) national team of Japan. They are playing so well during this World Cup and this is something that needs to be appreciated greatly."
Japan pulled off a stunning 2-1 comeback victory over Germany and were expected to beat a Costa Rica side who were demolished 7-0 by Spain in their opener.
"We weren't dead yesterday and we are still very much alive today, and we have to think about the next match on Thursday," Suarez said.
"We will have to play (against Germany) with the same pressure as in the past two games. But we are well alive, no one can forget about us just yet - we can still dream."
Victory over Japan, however, did not entirely erase the pain of their poor start.
"We were aware of what happened against Spain," the coach continued.
"I won't tell you what happened in the locker room, but we were very well aware of the situation. It was very painful for every one of us. Imagine coming to a World Cup and then losing in that way... It's not something that you adjust to easily.
"In the last few days, we worked much more than usual to get a victory today."
The fate of Costa Rica will be decided in their last group match, which is likely to be crucial for Germany as well.
"Today I still believe that basically we need to focus on how we prepare for the game on Thursday, make sure that the boys train the best they can - that's an important step," Suarez said.
"Moving on to the next stage only depends on us. It's a huge effort on our side. But as long as we make this effort, we'll be there."
