Madrid's bitter rivals suffered a 4-0 second-leg capitulation against Liverpool at Anfield on Tuesday to crash out 4-3 on aggregate at the semi-final stage.
Barca's wait for a sixth Champions League title will now stretch to a fifth year, having previously been knocked out in the quarter-finals in three successive campaigns on the back of lifting the trophy in 2015.
Zidane insists Barcelona's midweek heartbreak does little to improve the outlook of Madrid's season, though, with second place the best Los Blancos - European champions in four of the previous five years - can hope for in La Liga.
"You know how the season has gone for us and that will not change," Zidane said at Saturday's news conference when asked about the significance of Barca's Champions League demise.
"It is very difficult to win and we know what we did, which was impressive. It is special to earn four in five years. We value how hard it is to win it."
Zidane admits his side, who have finished top in just two of the last 11 seasons, need to place greater importance on the league.
"It is the day to day and allows you to do well in the Champions League and the domestic cup," he said.
"All the titles are important. The league allows you to be ready and compete in all the other competitions. Nobody will take away what we have done in the Champions League and how impressive it is. We value it very much."
Zidane also confirmed that Karim Benzema is in contention to return from a hamstring injury for Madrid's final away game of the season at Sociedad on Sunday.