Allardyce has warned that a new forward alone is not the answer to their sudden loss of threat in attack, with Everton playing out goalless draws against Chelsea and West Brom in their past two matches.
"We're consistently defending well, but on the opposite, we're not attacking very well in possession," Allardyce said.
"When I came in, they played out from the back, played through midfield and when they lost it, they lost a goal.
"When they went into transition, they couldn't defend properly and hence, conceded 25 goals in the last eight games before I got here.
"I think it's the reverse now. I think they are defending superbly well now but in transition they can't turn the ball into good passing opportunities and create more chances.