Babbel: Half-time tirade inspired Stuttgart
The Bundesliga side were fortunate not to be further than 1-0 behind but put up a much better fight in the second period to rescue a point and keep alive their hopes of joining the Spanish club in the last 16.
"Our performance in the first half was the worst I have seen from my team in quite some time," Babbel told reporters. "I had to raise my voice during the break because the first half defied belief," he added.
"I told them that we had to fight to stay in the Champions League and not to be so timid, and that I was the only one who had anything to be scared about."
Jesus Navas put Sevilla in front in the 14th minute at the Sanchez Pizjuan but the home side went down to 10 men with around 15 minutes remaining after they used all three substitutes and Aldo Duscher picked up an injury.
Zdravko Kuzmanovic delighted Babbel, who is under pressure due to the club's poor domestic form, by driving home a fine equaliser in the 79th minute.
Qualified Sevilla have 10 points from four matches, Unirea have five, Stuttgart three and Rangers two.