The Hammers only won two matches away from home during their relegation from the Premier League last season and Allardyce admits that their away form must improve.
They lost their opening match of the season 1-0 to Cardiff at home last weekend, which has increased the pressure to take all three points against Doncaster.
"Our away record is worse than poor," Allardyce said. "There’s massive pressure on us as early as game two.
"We go to Doncaster trying to make up as quickly as we can for getting nothing against Cardiff.
“We have to overcome the away-day blues at West Ham. It really is a big problem.”