Luiz Gustavo and Ricardo Rodriguez struck in the 58th and 72nd minutes respectively on Saturday to clinch Wolfsburg's two-goal victory, as Leverkusen slumped to a fourth straight loss in all competitions.
Leverkusen had equalised just before half-time through Sidney Sam but failed to respond in the second half.
"The goals scored by Luiz Gustavo and Ricardo Rodriguez were the deciding moments of this game," Kiessling said after the match.
"We always tried to get to the ball first, which we did well at times, but falling behind cost us dearly."
The defeat leaves Leverkusen on 43 points in second position in the Bundesliga table, 16 points adrift of leaders Bayern Munich and one ahead of third-placed Borussia Dortmund, who also lost on Saturday.
Meanwhile, Wolfsburg's fourth consecutive win in all competitions took them to 39 points and fifth position in the standings.
The northern club could move into the UEFA Champions League positions with another win next week but Gustavo maintained Wolfsburg are not getting carried away with long-term goals.
"We're only concentrating on our targets and our style of play. It's working really well right now," the Brazilian midfielder said.
"At the end of the day our aim is still to achieve something of note this season."
