Mali captain Cedric Kante says the Eagles deserved to win their quarter-final against co-hosts Gabon because of their "fantastic spirit".
The match finished 1-1 after extra-time and Mali eventually went through 5-4 on penalties, with Barcelona's Seydou Keita converting the winning spot-kick.
"I'm very happy, what a fantastic game," Kante told BBC Sport.
"It was a crazy scenario to win by penalties but I think we deserved it."
Gabon took the lead just after half-time through Eric Mouloungui and also hit the woodwork twice.
But Alain Giresse's side fought back and substitute Cheick Diabate scored the crucial equaliser in the 84th minute, after Gabon saw two gilt-edged opportunities from captain Daniel Cousin and Pierre-Emerick Aubameyang hit the post.
"Even if they missed two big chances to score, we played with fantastic spirit," said Kante.
"We didn't have this spirit until now but we are in the semi-final and our Africa Cup of Nations is now a big success."
Kante also believes the fitness of the squad was key to the victory.
"When we scored for the 1-1, I knew that they were tired," said the Panathinaikos centre-half.
"It was obvious and we wanted to finish the game before the end.
"After that we needed to be lucky to win on penalties and that's what we did. We are very happy."
Mali will now take on favourites Ivory Coast in Wednesday's second semi-final in Libreville and Kante admits that his side will be underdogs in the West African derby.
"Ivory Coast is the biggest team in Africa, so of course they want to win this competition.
"There is a big history between these two countries in football. Our fans will be watching us and they'll want us to beat Ivory Coast.
"We'll do all we can to beat this team even if we know they are strong."
Mali's victory ensured that they now boast the remarkable feat of having reached five Nations Cup semi-finals from just seven appearances at the tournament.
They have yet to win the trophy, with their best performance coming in 1972, when they lost 3-2 in the final to Congo.