The Bianconeri secured back-to-back wins to move up to 10th, having been winless and in the drop zone after their first four games.
Paulo Dybala and Leonardo Bonucci netted to give Juve a 2-0 lead before Maya Yoshida pulled one back for Sampdoria.
Manuel Locatelli added a third in the 57th minute with Antonio Candreva grabbing a late consolation for the visitors.
Juventus have scored 10 goals but also conceded 10 goals in six Serie A games this term.
“You have to work hard, have the pleasure of defending and not conceding goals, it’s something that is as much a part of football as possession,” Allegri said.
“We haven’t conceded many chances, the problem is that we should be conceding fewer goals.”
Juventus, who are due to play Chelsea in the UEFA Champions League in midweek, are on the improve according to Allegri.
“This is a difficult time in terms of mental and physical fatigue, but slowly, slowly we are moving up the rankings,” he said.
“Today’s victory must make us understand that we must suffer at times, like we did in Spezia, now we need a clean victory, which would further increase our self-esteem.”