Arsenal battled to a 2-1 victory at Manchester United on Monday to book their place in the FA Cup semi-finals, but face the daunting task of coming from 3-1 down at Monaco in the second leg of their UEFA Champions League last-16 tie next Tuesday.
With his side sitting third in the top flight, Wenger recognises the pressures that come with fighting for silverware on three fronts, but says it is time for his players to make a name for themselves.
"We can only help so much, 99 per cent is down to the individual," he told arsenal.com. "We can push them over the line with the one per cent we can give, but 99 per cent is them having the responsibility to make their own life.
"You have to stand up to be strong enough, to fight, to show that you have the courage and that you're not inhibited because you're under pressure, and that's the difficulty of the modern player.
"That has increased and the resistance to stress from the young players is immense today because everything is analysed. Every pass you make, every first touch, how far you run, how much you fight, everything."
Arsenal, aiming for a fifth successive Premier League win, received plenty of plaudits for their performance at Old Trafford on Monday and West Ham boss Sam Allardyce is braced for a tricky encounter at the Emirates Stadium.
"I watched Arsenal's game away at Manchester United and everyone could see the quality they have," he said. "We know how difficult it is at the Emirates, where we've actually gone in front a few times but not managed to hold on.
"We'll go there and give it our best shot and see what happens. I think they have different threats from all over the team, which is why they are so difficult to beat, especially at home.
"We conceded two goals very quickly in the reverse fixture [Arsenal were 2-1 winners at Upton Park in December] which was the only difference between the two teams on the day."
Arsenal remain without the services of Gabriel Paulista (hamstring), Jack Wilshere (ankle), Mikel Arteta (ankle), Mathieu Debuchy (shoulder) and Serge Gnabry (knee), while there are doubts over the availability of Alex Oxlade-Chamberlain, who injured a hamstring against United.
West Ham's biggest injury concern is Enner Valencia, who cut his toe on a broken cup in an accident at home, and Winston Reid is set to miss out due to a hamstring problem. Former Arsenal midfielder Alex Song is struggling with a knee issue and Carl Jenkinson is ineligible to face his parent club.
A run of one win in their last 11 Premier League games has left West Ham 10th.
