Inoue began his motorsport career in the British Formula Ford Championship in 1988. He then spent four seasons in All-Japan Formula Three from 1989 to 1993 before contesting the International Formula 3000 championship in 1994. His F1 opportunity came late in that same year, when Simtek invited him for a one-off appearance at the 1994 Japanese Grand Prix, from which he retired.
For the 1995 Formula One season, Inoue secured a full-time seat with the Footwork Arrows team, partnering Gianni Morbidelli for most of the year before Max Papis replaced Morbidelli late in the campaign. Despite the lack of points, Inoue occasionally outpaced Papis, a driver with a stronger pedigree in single-seaters.
His F1 tenure produced no competitive results but generated two incidents that became widely discussed.
The first occurred after a practice session at Monaco: his stalled car was being towed back to the pits when a course car driven by Jean Ragnotti struck it, causing the car to roll into the barriers. Inoue was uninjured and raced the following day.
The second, and more widely seen, incident unfolded at the 1995 Hungarian Grand Prix and was broadcast live worldwide. After engine failure forced him out of the race, Inoue climbed out to help marshals fight an engine fire. A Tatra 623 safety vehicle driven by a marshal then struck him as it arrived on the scene, injuring his leg. He recovered in time for the next event.
Entering 1996, Inoue pursued a drive with the Tyrrell team, but the team chose Ukyo Katayama, who brought Mild Seven sponsorship from Japan Tobacco. Inoue was then announced as a Minardi driver for 1996, but one of his personal sponsors withdrew at the last minute, forcing him out of the sport. Minardi replaced him with Giancarlo Fisichella.
After leaving F1, Inoue briefly competed in sportscar racing before retiring from professional driving at the end of 1999. He subsequently worked as a driver manager in Japan.
Inoue's candour about his own abilities became a distinct part of his public persona. He publicly described himself as the "worst driver in Formula One," admitted he initially had no idea what a pit stop was, and told Top Gear magazine in 2015 that he was "not good enough to drive in F1." Following Nico Rosberg's retirement at the end of 2016, Inoue posted a tongue-in-cheek advertisement on Twitter offering himself as a replacement, detailing his F1 incidents in a self-aware tone that won him considerable new attention on social media.
His willingness to discuss his own shortcomings with humour rather than defensiveness made him an unusual and enduring figure in the sport's popular memory, recognised long after more successful contemporaries were forgotten.