The Swiss manager said she was disappointed with the result but reserved praise for her players for the fighting spirit and character they showed.
Ghana lost 1-0 to the Copper Queens in the first leg at the Accra Sports Stadium before holding the southern African country to a 3-3 draw in Ndola on Wednesday.
During the second leg, the Black Queens came back from behind twice before taking a lead going into the final 15 minutes of the game.
Goals from Barbra Banda and Kabange Mupopo had been cancelled out by strikes from Gifty Assifuah and Doris Boaduwaa, with Doris Abugre’s long-range effort giving the Black Queens a 3-2 lead.
And the game looked to be heading towards extra time before Jennifer Cudjoe was sent off in the final minute of added time with a second yellow card after stopping a promising attack.
From the resulting free-kick, Banda smartly smashed the ball low and hard into the net, beating Ghana’s wall to make it 3-3 on the day and 4-3 on aggregate.
Although the result saw the Black Queens once again miss out a place in the Olympic Games, Hauptle was proud of her players’ performance.
"My team was brave, my team was playing football, my team was fighting, I can't blame them at all. Sometimes it's hard,” Häuptle said after the game, as quoted Ghanafa.org.
"They scored a free kick and the red card in the last minute. We would have loved to go overtime but all in all it's disappointing for us but kudos to Zambia.”
Meanwhile, Ghana will now turn attention to the 2024 Women’s Africa Cup of Nations (WAFCON), which will be hosted by Morocco in August.