The 25-year-old, who joined from Liverpool for around โฌ30m over the summer, made his Inter debut as a substitute against Cagliari before being introduced at the start of the second half in place of Petar Suฤiฤ against Napoli, delivering an impressive display as Cristian Chivu's side came from behind to win 3-2.
Speaking to CBS Sports before the match, Jones reflected on how smoothly he had settled into life in Italy despite the change of country and league.
"I feel like I'm at home. I'm just being myself," he said. "I love the players, the fans. I enjoy myself during the game, and the staff are all great too."
After the final whistle, Jones spoke to Inter TV and struck a similarly positive tone about his early impact at the club.
"I'm really happy to be part of the team, it was a difficult match and the fans pushed us on in a brilliant way โ a great win," he said.
"I want to be part of this team, I'll try to always give my best when I'm called upon."
Jones was also asked about Inter's prospects against Real Madrid, with the two sides set to meet later in the season.
"We're confident, we never give up," he said.
The Englishman's rapid adaptation will come as a relief to Inter, who moved decisively for his signature after seeing off competition to bring him to San Siro as part of a wave of Premier League arrivals this summer, alongside John Stones and Djed Spence.
Jones spent 16 years at Liverpool after joining the club's academy aged nine, making 228 appearances and winning two Premier League titles among a host of other honours before deciding it was time for a new challenge away from Anfield.
Napoli had threatened to derail Inter Milan's start to the season, but Chivu's side showed the resilience to fight back and secure a fourth win of the campaign, with Jones' introduction at half-time proving a turning point as the hosts wrestled back control of the match in Milan.