Sunday's victory over rock-bottom Parma ended their five-match winless run in the top flight, but the three points still only leaves Filippo Inzaghi's side eighth in the table.
With Milan five points off the final European spot, Tassotti told reporters on Friday that it was "fundamental" for the club to be challenging among the frontrunners again.
"Perhaps we underestimated some of our opposition and we cannot allow ourselves to do that with any side," Tassotti explained, covering at the news conference for the unwell Inzaghi.
"We've also been lacking in confidence. The match against Parma was an important moment and on paper it was an easy match, but for us in that moment it wasn't easy to collect all three points.
"We were able to win and we now want to build on that and continue playing good football. We played well against Napoli and Roma, but then we lost our way.
"We would always like to play an attacking game but it also depends on our opponents that often force you into playing a different type of game.
"It's fundamental that this club gets back to competing for the top places. This is what we want."
Milan face Juve and former coach Massimiliano Allegri in Turin on Saturday looking to beat the leaders for the first time since 2012.
"This Saturday's match is the hardest match that we could have faced, but this is what the fixture list has thrown up," the former Italy international explained.
"It's never been easy in Turin, even for the Milan sides coached by [Arrigo] Sacchi and [Fabio] Capello.
"It's a tough ground to play at, but we are ready to battle. In football you go through these negative moments, even Juventus experienced them before they got back to being successful.
"Juve are a side that drop very few points and concede very few goals. They are capable of changing from one playing system to another easily and Allegri has done well to gradually bring his own ideas into an already settled context.
"If we are organised and aggressive for 90 minutes we have a chance."
