The Liverpool player put England ahead with a ninth-minute penalty, his third goal in three international outings, but was forced off mid-way through the first half, with Theo Walcott coming on.
"He's being assessed by the medical team. It was a great shame because I've really enjoyed working with him," Southgate told his post-game press conference.
"He's an intelligent, very talented footballer who's adding goals to his game for England.
"He was quite key to how we were wanting to play, but great credit to Jesse (Lingard) for moving positions and picking the role up as intelligently as he did."
Lallana, however, appeared to offer a positive assessment of his condition as he walked through the mixed zone, telling journalists: "It's OK."
Jamie Vardy's 48th-minute diving header doubled England's lead at Wembley, but Spain debutant Iago Aspas reduced the arrears in the 89th minute before Isco equalised in the sixth minute of added time.