The Bianconeri maintained their seven-point lead at the top of Serie A with victory, secured by Gonzalo Higuain's brace, but Allegri's men struggled at times in Sardinia.
With the hosts down to 10 men for the final 23 minutes, the Juve coach had hoped to see the visitors add to the scoring - and acknowledges they must be better against Champions League opposition.
"I want a spectacular Juventus," he told Sky Sport Italia. "When you play football, you need to be spectacular. Cagliari went down to 10 men and we should have run riot.
"Instead, we were hasty and didn't make the right choices. We need to improve. At a certain stage, we took our foot off the gas and allowed Cagliari to have several chances, which should not happen.
"The team has to be spectacular, yes, but also effective, because there's no point if you don't win. The best players in the world play it simple. The trouble is that it's more complicated than it looks to play it simple.
"With this system, we have more room to breathe and the pitch feels larger for us, but we have to be better in defence and attack in the Champions League. We cannot afford mistakes."
Allegri did reserve praise for Higuain, though, acknowledging the work the Argentina international does beyond scoring goals.
"Higuain is an extraordinary finisher, but we always knew that," he added. "The really impressive thing is how hard he works for the team."