Despite twice taking the lead, the Teranga Lions ultimately settled for a point as the Samurai Blue hit back on both occasions in the Group H fixture at Yekaterinburg's Central Stadium.
Sadio Mane opened the scoring for the West Africans in the 11th minute before Takashi Inui drew parity 23 minutes later. On 71 minutes, Moussa Wague put Senegal 2-1 up but the lead only lasted for seven minutes as Keisuke Honda drew Japan level.
"We conceded two goals that were avoidable – that was clear. We were not very good, frankly speaking," Cisse said.
"The [better] team on the pitch was the Japanese team. They played well, controlled the match but we managed to score two goals and take a point.
"We were not concentrated enough. What is annoying for me is the two goals we conceded."
After 2-1 wins in their opening games, Sunday's result has left the Teranga Lions and the Samurai Blue tied at the top of the table with four points apiece, one more mark than Colombia, who handed Poland a 3-0 reversal in the other group game.
“They [Japan] played as we expected," Cisse remarked.
"They are a very technical team with high passing quality.
"We started the game very well and exerted pressure, pushed them out of their comfort zone, made them make a lot of errors and we exploited that, scoring first."
Senegal, who take on Colombia in their last group game on Thursday, need just a point to confirm their place in the round of 16.
“We hope to qualify," Cisse added.
"We didn’t play great today but we didn’t lose.
"We have to believe and have confidence. We have the quality necessary to beat Colombia.
"It is going to be hard-fought. We hoped to have qualified on Sunday but it didn’t happen and it’s up to us to get it right against Colombia."
The Teranga Lions are on their second appearance at the World Cup.