The relegated Tigers fell behind early on in their first game back in the second tier, but Jarrod Bowen's equaliser shortly past the hour mark rescued a point in Slutsky's first competitive match at the helm.
The Russian admitted that his team are still adapting to life in the Championship, and believes they were worthy of the draw despite Villa missing a host of chances to take all three points.
"It was a difficult time for me and my team, a lot of us are new to the Championship. There were a lot of firsts. Aston Villa is a big team, it was a full stadium and a very good atmosphere for them at home. It made it difficult for us," he told reporters.
"But we will adapt after more matches. We played very well and created some good chances and in the end I think we deserve this result."
Hull will host Burton Albion in their first home game of the season next weekend.