The Hammers begin their Europa League campaign away to Croatian champions Dinamo Zagreb
With the additional competition creating a packed schedule, manager David Moyes moved to strengthen his squad just before the transfer deadline by recruiting a trio of internationals.
Creative Croatia playmaker Vlasic made his debut as a second-half substitute in Saturday’s 0-0 draw at Southampton, while France defender Zouma and Czech midfielder Kral were unused substitutes.
The St Mary’s stalemate marked the first of seven games in just 23 days for the London club and Bowen has welcomed the increased competition.
“It’s building on what we achieved last season,” the 24-year-old told West Ham’s website.
“We’ve got the Europa League this season as well and with the players we’ve signed and the stature they’ve got, they’re only going to help improve the team.
“That’s what we want: we want competition for places, we want as many players as fit as we can because we’ve got a lot of games this season, and we want to make it a special one.”
Ex-Hull winger Bowen went closest to a West Ham winner on the south coast when his second-half volley was tipped over by Southampton goalkeeper Alex McCarthy.
But the Hammers – who missed the chance to go top of the table – were fortunate to escape with their unbeaten record intact after lively Saints substitute Armando Broja hit a post before seeing a late header cleared off the line by Declan Rice.
Moyes’ men were then deprived of the services of the top flight’s August player of the month Michail Antonio for next weekend’s clash with Manchester United after he was sent off for a second booking deep into added time.
“It was one of those afternoons where we had a lot of the ball but ultimately in the final third – where we’ve been really good recently – we were a bit off,” said Bowen.
“It’s disappointing but, when you’re not fully at it, keeping a clean sheet and getting a point away from home has to be looked at as a positive.”
Southampton’s clean sheet was their first of a campaign which is still to bring a league win.
Antonio, the top-flight’s leading scorer, was well shackled by a combination of Jack Stephens and Mohammed Salisu.
Ghanaian Salisu has been a regular so far this term, having been restricted to just eight Premier League starts last season after his £10.8million arrival from Spanish side Real Valladolid.
Saints boss Ralph Hasenhuttl has been impressed with the 22-year-old’s physicality but is eager to develop his technical attributes in the wake of Jannik Vestergaard’s summer departure to Leicester.
“On the man he’s very strong. In the duels he’s very nasty because he’s on them and this is his game,” Hasenhuttl said of Salisu.
“He still has to improve his game with the ball, that can be much better but we are going slowly this way. It’s not something we learn from one day to the other.
“We force him to play more football, he didn’t do it so much in his career so far but this is what we want.
“He’s not a Vestergaard so far with the ball but we want to improve him and finally I’m happy for both centre-backs that they have their first clean sheet this season.”