The result leaves the Reds four points adrift of the top six with six games left to play and Slomka no longer fancies his side's chances of bridging that gap in their remaining Bundesliga fixtures.
Hannover travel to fifth-placed Freiburg next weekend before hosting Bayern Munich.
They also travel to Greuther Furth and Bayer Leverkusen and host Mainz before ending the season at home to Fortuna Dusseldorf.
"We need not have any European ambitions anymore," he told LIGA total! television.
More than the four-point deficit, it was his side's performance which has convinced him that his players will be watching the Europa League from their own living rooms next season.
"We have got to play in a different way to this," he said. "The first half could have put me to sleep.
"We had the chance to move closer (to the top six) in front of 46,000 fans today [Sunday], but it was a fully deserved point for Stuttgart and a disappointing one for us."