Real have been drawn to play Galatasaray in the Champions League quarter-finals next month, and Terim was in the stands at the Bernabeu when relegation-threatened Real Mallorca twice took the lead in the first half.
Mallorca's first came from a header and the second from a familiar failing for Jose Mourinho's men, when a corner was flicked on to the far post and Alejandro Alfaro was left unmarked to head past Diego Lopez in the 21st minute.
Real rallied with three goals in six minutes at the start of the second half from Cristiano Ronaldo, Luka Modric and Gonzalo Higuain but Real director Emilio Butragueno expressed his concern in a post-match interview.
"Today, in the league, there was room to react but in the Champions League one goal could be decisive," Butragueno told Spanish television.
"We need to be vigilant at these plays."
Mourinho's assistant Aitor Karanka was also questioned about Real's continuing problems at defending dead-ball situations.
"These plays have been troubling us since the start of the season, they are lapses in concentration," he told a news conference.
"We will try to improve. It is in our hands. Luckily these errors haven't been important in the long run for today's final result, but we must draw conclusions."
Real have made it clear their priority this season is the King's Cup, where they meet Atletico in the May 17 final, and the pursuit of a possible 10th European crown.
Real host the Turkish league leaders in their quarter-final first leg on April 3, and travel for the second leg on April 9.
Saturday's league victory left Real in second place 10 points short of leaders Barcelona, who host Rayo Vallecano on Sunday, and four ahead of third-placed Atletico Madrid, who visit Osasuna.
"The message remains the same," Karanka said. "It is very tough to reach the top spot, and we don't want to complicate life with the team below us. We have to make sure of second place."
- Sports & Recreation
- Real Mallorca
- Champions League
- Emilio Butragueno
- Jose Mourinho
- Aitor Karanka