The Hammers reinvested the £105million for the sale of former captain Rice in deals for Ward-Prowse, Alvarez, Konstantinos Mavropanos and Mohammed Kudus as the club won three of their opening four games.
Talking about Rice on Rio Ferdinand's VIBE with FIVE, Bowen said: "I was gutted, but it was always the saga every window: 'was Dec going, was Dec not going?'.
"To replace Dec is impossible, you see what he does for England, what he's doing for Arsenal, his quality speaks for itself and showneven more people what he can do.
"But we have always bought the right people to fit the dressing room ... the manager is really tight on that culture in the dressing room to bring out the best results.
"Who we have brought in, with Edson Alvarez and James Ward-Prowse, it looks like they are been there for five years, and everyone has made them feel so welcome. It's a club which is easy to get into a group, which is why they have hit the ground running."
Ward-Prowse has two goals and three assists in five games for West Ham, while Alvarez made clear his intentions in his first training session with the squad.
Bowen continued: "People probably only think he is good at set-pieces, but you see his quality in games and how he affects games.
"Edson as well, in his first training session I was like 'this guy just wants to smash everyone'. He was just running around clamping everyone in sight and we were like 'this is what he need, we need a bit of fight in the middle', especially after losing Dec.
"For life without Dec, we had to invest in wisely because we knew the quality of player we were losing. It's difficult to find a direct replacement for Dec as I don't see many better than Dec for what he does. We've started really well and the signings have played their part, they've really helped the team."
"Dec has a bit of everything. He can play holding, but also get into the box and travel with the ball."