Inui, who signed for Real Betis at the start of June, has been one of Japan's most influential players at this World Cup and was once again a constant threat down the left flank in the Group H encounter.
He scored Japan's first equaliser with a delightful curled finish, set up Keisuke Honda for Japan's second 12 minutes from time and also hit to crossbar with another second half effort.
Despite his personal performance, Inui echoed the words of his coach Akira Nishino in expressing disappointment that Japan did not get the win that would have put them in control of the group.
"It was a game we could have won and I think there would have been a different outcome if I had scored a second (with his shot that hit the bar)," Kyodo News quoted Inui as saying.
Inui, who also scored twice in a pre-tournament win against Paraguay, blamed himself for the second Senegal goal.
"Their second goal was down to my marking. I have to be a bit more focused (in those situations).
"But I am scoring in recent matches the way I did today and I wanted to get a shot in somewhere from that kind of position. I really just let fly with the shot and am glad that I got a result out of it."
Japan go into their pool final match against Poland on Thursday knowing a win will guarantee their safe passage to the Round of 16.
"Poland are going to be a difficult team to beat," Inui said. "Hopefully we can pull together and make a killer effort."
(Reporting by Jack Tarrant; Editing by John O'Brien)
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