The Turkey international was signed from Besiktas for a fee of £27m last month with the promise of goals aplenty, having found the net regularly during his time in the Super Lig.
Tosun's career in English football has not quite taken off so far, though, being used for a combined total of 196 minutes since joining more than five weeks ago.
Allardyce left the 26-year-old on the bench in Saturday's 3-1 win against Crystal Palace, but still remains hopeful of seeing more from the goalless striker over time.
"He is struggling with the pace of the Premier League which happens to more players than it doesn't who come in in January," he told reporters at his post-match press conference.
"He was up to scratch when he was playing but there is more demand at this level to get to the level and show the ability he has got. There is no doubting his goalscoring ability but you have to have the capabilities to get in those positions to score those goals and that is the hard bit."
Everton are due to fly out to Dubai on Wednesday for a warm-weather training camp, before facing Watford on February 24 in their next outing.