While Roberto Di Matteo's side beat the holders 4-3 on the night, Real progressed on aggregate, leaving Schalke with only the Bundesliga to focus on this term.
A run of just two wins from their last six league outings has seen Schalke slip out of the top four, although captain Howedes - who was almost the hero late on at the Santiago Bernabeu - insists his side can take momentum from the last-16 exit.
"I had a good chance towards the end, but unfortunately couldn't get enough power on my shot, which is really annoying," he told the club's official website.
"Despite being eliminated, I'm proud of the guys. Everyone gave it their all and showed that we can play good football.
"[Wednesday's] game gives me a lot of hope for the coming weeks. We now need to recover as quickly as possible because it was intense."
Bayer Leverkusen - who have assumed Schalke's top-four berth in - get the weekend's action under way against bottom side Stuttgart on Friday before leaders Bayern Munich travel to improving Werder Bremen.
The champions moved into the quarter-finals of the Champions League with stunning 7-0 victory over Shakhtar Donetsk on Wednesday and can move 14 points clear provided Wolfsburg are beaten by strugglers Freiburg.
Following his infamous celebration with Hennes the goat, Cologne's Anthony Ujah will hope to have further cause for joy Signal Iduna Park.
Peter Stoger's side stand in the way of Borussia Dortmund extending their unbeaten league run to six and potentially moving into the top half.
It would represent another reference point in Dortmund's upturn of fortunes, following a dismal first half to the campaign, although they will require Paderborn to take something from their trip to Eintracht Frankfurt.
Hamburg continue their battle to avoid the drop as they seek a first win over Hoffenheim in four attempts, while Augsburg host Mainz after their victory against high-flying Wolfsburg last time out.
Borussia Monchengladbach and Hannover round off the weekend's action when they meet at Borussia Park in Sunday's late kick-off.
