Milan were held at the San Siro by Bologna on Sunday after Zlatan Ibrahimovic rescued a point with a 90th minute equaliser. Milan host Genoa on Wednesday having taken just one point from their last two home matches, which Allegri says is unacceptable.
"We've got one point from our last two home games and we needed to get more than that," said Allegri.
"We started well [against Bologna] but then we gifted them a goal and became disorganised. We created a lot in the second half but we didn't manage to win.
"On Wednesday we have another home game and we need to try to win regardless of what Juve do, not least because second place isn't mathematically secure. And you never know in football."
Milan find themselves three points behind league leaders Juventus in Serie A.