Real's loss at a stunned Bernabeu on Saturday, which spoiled their perfect home record of 14 wins this season and ended coach Jose Mourinho's own nine-year unbeaten run in home league games, severely dented their hopes of ending Barcelona's two-year reign as Spanish champions.
Barca's 1-0 win at Villarreal stretched their lead to eight points with eight matches left and they have what looks to be a significantly easier run-in to the end of the season.
"We will see what happens in La Liga but the priority right now is to concentrate on Tottenham," goalkeeper Casillas told reporters at the Bernabeu.
"We have to absorb the blow and regroup," he added. "It's always hard to digest a defeat but we will deal with it as best we can and with a desire to get the best out of the rest of the season."
Real's joint La Liga top scorer Cristiano Ronaldo, in-form striker Karim Benzema and full-back Marcelo all missed the Gijon game through injury, while midfielder Xabi Alonso was suspended, and they lacked creativity against a stubborn opponent.
Mourinho told a news conference he might risk Ronaldo on Tuesday. The world's most expensive player, who is level on 27 league goals with Barca forward Lionel Messi, has a leg muscle strain and was left out of the squad for Saturday's game.
Benzema would not return to action until next weekend's La Liga match at Athletic Bilbao and fullback Marcelo would be sidelined for two weeks, Mourinho added.
"If we are solid and we don't have offensive problems we have a good chance of winning," said the Portuguese, who won Europe's elite club competition with Inter Milan last season. "At home, it's no drama if you draw."
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1