The Hammers have had a poor start to the season, suffering back to back defeats under new manager Manual Pellegrini.
The boss has brought in nine new players and he gave four of them debuts against Bournemouth, as the Cherries were able to come from behind to win 2-1 in London.
"We have got a lot of new players and we need to gel," Wilshere told the West Ham official website.
"At this level in this league, people aren't given time, so we have to do it quick and all tuck in this week."
"We started well and we all wanted to win this week and we felt we were good enough to win. Obviously, the dressing room was devastated because we should have come away with something from the game, but we have to go again."
"That's the thing about this league, you haven't got much time to be down. You have to be back on the training pitch and go again."
West Ham will face Wilshere's former club Arsenal next, who are also yet to pick up any points in the new season.
"It won't be easy next weekend," Wilshere admitted. "We've had a tough start but you have to be willing to fight against anyone in this league and win your duels and earn your right to play, and I felt we did that at times."
"We played as a team, but we let in two sloppy goals."
Bournemouth's Wilson and Joshua Kin posed problems for the side throughout the game.
"Callum did really well for us, his partnership with Joshua King is developing in a way we wanted it to last season," Bournemouth manager Eddie Howe told reporters.
"Joshua was strong as well but they both set the platform for our performance."
"I was really pleased with the team, we managed the game very well and it was a great win. We'd never won there before so it's a good moment for the club."