Wenger said: "Dennis Bergkamp is not at his best at the moment, he knows that. But it is mainly physically because he only started training on 1 August and had a small setback injury-wise against Manchester United in the Charity Shield.
"And he has played just two games now - one last Monday against [Nottingham] Forest and one at Anfield. He's not as sharp as he used to be, but that is a question of time. For us it is important to get our players slowly back to full fitness without us dropping too many points."
Wenger is also worried that later in the season the stamina of Bergkamp and fellow Dutch international, Marc Overmars, may be affected after two seasons of near-continuous football.
But he feels that the French midfielders, Patrick Vieira and Emmanuel Petit, have the ability to stay fit despite their part in the host nation's success.
He said: "It's not quite the same for the other World Cup players because up front you need to be really sharp to make a difference but in midfield they have the stamina.
"We might have a different problem with Bergkamp and Overmars later on in the season because they need more stamina and physical power by then. So they could have a problem around October and November with overall fitness. But for Dennis it's a question of sharpness and overall fitness - two different problems, really."
The Liverpool co-manager Roy Evans is also worried about the fitness of his World Cup players, with the England striker Michael Owen entering his second full season at the age of 18.
He said: "Most clubs are in the same position. Before the season started we decided that everybody should get at least three weeks' holiday, maybe a touch more, if they could. It's important for the rest of the season. Lads came back from the World Cup later than the rest and it will take them a week or two more to regain their sharpness. It's just that extra 5 or 10 per cent that makes them the great players that they are. The effort is there but they all need that little bit more edge."
The former Tottenham captain, Gary Mabbutt, has appealed for Spurs fans to give the manager Christian Gross more time as they continue to turn against him and chairman Alan Sugar in increasing numbers.
Tottenham's 3-0 weekend defeat at home to Sheffield Wednesday, following a 3-0 defeat at Wimbledon, led to angry demonstrations at White Hart Lane on Saturday, calling for Gross and Sugar to quit the club.
An offer from the former Atletico Madrid manager Raddy Antic to take over, as well as a report that Sugar was driven to the point of deciding this week whether to sell his stake in the club, have hardly helped matters. However, Mabbutt feels that it is far too early in the season for pressure to be mounting on the Swiss head coach, given that this is Gross' first full season in charge.
The Tottenham stalwart, who left the club in the summer, said: "I totally understand the fans' frustrations as they have been starved of success for the past six years and have been living in Arsenal's shadow. But even in the harshest of circles, you can't be talking about managerial changes after just two games."
Mabbutt added: "The fans will obviously voice their opinions and I'm sure that the manager and chairman understand their feelings."