The Germans were held to a draw by Steaua Bucharest on Tuesday, which means they will go into the meeting with their Swiss rivals in Gelsenkirchen needing a victory.
The Germans were held to a disappointing draw at Steaua Bucharest on Tuesday night and that result, coupled with their Swiss rivals' surprise win over Chelsea, has left the Bundesliga outfit third in Group E.
However, despite the disappointing result in Romania, Howedes is in no doubt that Schalke will rise to the occasion against Basel in Gelsenkirchen.
"We are under pressure, but we can handle it," the defender said. "We now just have to focus on winning the game against Basel. I think that we left a lot of good opportunities unused out there, but we also got lucky on a few occasions."
Schalke goalkeeper Ralf Fahrmann, who made his tournament debut in place of the injured Timo Hildebrand, took some positives from the draw.
"We struggled to get into the game," he said. "We wanted to win here, so it is a disappointment despite having picked up a point. It is always important for a keeper to keep a clean sheet but nonetheless I would have liked to win the game."
Midfielder Julian Draxler, who made an appearance off the substitute's bench after struggling with flu, echoed the sentiments of his skipper.
"We now have a decisive match against Basel at home and simply have to win that," the youngster said. "We would have liked to seal the deal but even after this draw our situation has not really changed."