Stuttgart were humbled 2-1 at home to Schalke 04 on Saturday, their third straight defeat in the German league, which leaves them 13th in the table and struggling for confidence.
Sevilla also went down 1-0 to Deportivo La Coruna on Saturday to go third in the Spanish league, but Babbel saw enough in the defeat against Schalke's Royal Blues to take some heart for Tuesday.
"The team fought hard and showed heart against Schalke," said Babbel. "We made some crucial errors at key moments, that was very annoying, but our performance gives us confidence ahead of Tuesday's game against Sevilla."
Having been pegged back by a late equaliser at home to Rangers in a 1-1 draw in their opening round of Group G matches, VfB Stuttgart will be determined to avoid another slip when they host the Spaniards.
After seeing his side go down 1-0 to Deportivo, Sevilla boss Manolo Jimenez was keen to add some perspective to the result.
"We are not going to be relegated after losing to Deportivo," said Jimenez.
Jimenez also dismissed suggestions that Sevilla had missed striker Luis Fabiano saying: "Everyone has things to improve on. The rotations worked well, and we put in a good performance."
Stuttgart are second in the section on two points, having also drawn 1-1 at Unirea Urziceni, while leaders Sevilla followed up their 2-0 home victory over the Romanian titleholders by triumphing 4-1 at Glasgow Rangers.
It is an early reunion for teams who met 12 months ago in Spain during the UEFA Cup group stage when Sevilla won 2-0.
Stuttgart have not won in three games at home to Spanish opponents and failed to even score in their last two fixtures. The draw with Rangers at least helped Stuttgart improve their home record in the Champions League.
Before that they had lost three of their last four games in their own stadium.