The Bundesliga outfit laboured to a 0-0 draw against their Spanish opponents, failing to create much in the way of goal scoring opportunities against a squad which included Euro 2012 winner Alvaro Negredo.
After a fantastic league campaign last year, Gladbach will compete in the Champions League qualifying rounds in the coming weeks, but the trainer was insistent that his side must improve against teams of Sevilla's class if they are to stand a chance of progressing to the group stage.
"We have to move much more quickly," Favre stated to Bild. "Otherwise it is clear that against such teams no chances will come."
Gladbach take on Norwich City next weekend before beginning their domestic season with the DFB-Pokal clash against Alemannia Aachen on August 18.