Vahid Halilhodzic's men were brave 2-1 losers to Germany after extra-time on Monday, as Joachim Low's side scored at either end of the extra half-hour to progress to the last eight.
Bougherra revealed Halilhodzic told his team to play freely at the half-time during regulation, but said the north African nation were immediately looking forward to continental glory after falling short on the world stage.
"At half-time, the coach asked us if we really believed in us and wanted us to continue to play ball without hesitation," Bougherra told beIN Sports.
"After that, it was a bit difficult at the physical level but we could have come out with a draw and go at least on penalties.
"Now, the next goal is to win the Africa Cup of Nations."
Bougherra hailed Bosnian tactician Halilhodzic for helping the Group H minnows defy the odds and reach the last 16.
"And on behalf of all players, I want to pay tribute to Vahid. He took the team from the lowest (point) and did a great job. It is good for the whole of Algeria. We can be proud of this team," he said.
"Thank you to all those who worked hard for us. Algeria is a good team, now we are respected. It is hoped that the value of all the Algerian players will rise, because we deserve it and we are a little underestimated.
"There are many positives. Also thank you to the Algerian public, which has always been behind us. And Brazilians have always supported the team. "
Man-of-the-match in Porto Alegre, Algeria goalkeeper Rais Mbolhi said he was disappointed to exit Brazil but also had kind words for coach Halilhodzic.
"We played against a very strong Germany team and conceded two goals late on," Mbolhi said.
"We're very disappointed because we felt we had a chance. Fitness wasn't the decisive factor.
"We're part of Algeria's footballing history because we're the first team to have come this far and we can build on this for the future.
"We owe it to our coach that we made it into the round of 16. We'd like to thank him for everything he's done for and with the team."
