The England defender opened the scoring as City saw off their Manchester rivals with a 2-0 win at Old Trafford to book a place in their fourth successive final in the competition.
Bell, considered one of the club’s greatest ever players, passed away at the age of 74 on Tuesday.
“I’d like to send our condolences for Colin Bell and his family,” Stones told Sky Sports.
“I think how we played today was a reflection of him. A great moment for us and hopefully he is looking down on us. It was a great occasion, another win against another of the top teams.”
Stones’ goal was the latest sign of his return to form, the England international enjoying a renaissance this season at the heart of the City defence alongside summer signing Ruben Dias, who was man of the match at Old Trafford.
“I’m just working hard, just trying to play as many games as I can,” Stones added. “I want to give everything to the team and stay true to myself – see what I can do, what I can improve on.
“Playing these big games is something I thrive off and I just want to play well.”