The visitors lost 2-1 to Viktoria Plzen on Thursday but their 5-3 advantage over two legs ensured that they join the likes of Juventus and Benfica in the Europa League last eight
Bafetimbi Gomis' first-half strike made it 5-1 on aggregate and progress for the Czech side looked unlikely, although two goals in the second half from the hosts saw the Ligue 1 giants beaten on the night.
Garde admitted it was nerve-racking as the match wore on, but reserved praise for goalkeeper Anthony Lopes for ensuring that Lyon battled their way into the quarter-finals of the competition with a 5-3 aggregate triumph.
"We sealed qualification and we got what we wanted even though it was scary in spite of ourselves," the coach told reporters.
"Anthony Lopes was fantastic between the sticks. He made wonderful decisions that kept us in the game."
Lyon join the likes of Juventus and Benfica in the last-eight draw, which takes place on Friday, and it is the first time that the French club have reached this stage of the tournament since 1998-99.