The Bianconeri were linked with players such as Toni Kroos, Radamel Falcao and Alexis Sanchez over the past few months but, in the end, their most noteworthy addition was Alvaro Morata, who arrived from Real Madrid for £16 million.
Allegri insists that he is happy with the strength of his squad but claims that some players are simply out of Juve's reach.
"I had an agreement with the club that we would only strengthen the team with players who could really add something," Allegri told reporters.
"We eventually didn't sign anyone else, but that wasn't because we didn't want to strengthen. It's because there are big clubs out there with a different budget than Juventus.
"It's enough to look at what clubs like Barcelona, Real Madrid and Manchester United have done this summer.
"It would not have added anything if we'd signed players we wouldn't have used. I am convinced that we already have a good squad to do well in the Champions League."
Juventus started the 2014-15 Serie A campaign with a 1-0 win over Chievo at the weekend.