Juventus, who are aiming to bag six consecutive league title, are considered overwhelming Serie A favourites and also a strong contender in the Champions League following a string of impressive signings in the summer.
They won the first two matches easily but drew 0-0 against Spanish club Sevilla and then lost on Sunday to Inter Milan.
Following the loss at the San Siro, Allegri stressed that his charges now had to keep their feet on the ground and roll their socks up again for a busy period of fixtures, which see them take on Cagliari, Palermo and Dinamo Zagreb over the next nine days.
"We now have a run of important matches and we need to return to winning ways, remembering that we have to do the business on the pitch in order to secure the results we want," the Juventus tactician said.
The 49-year-old pointed to plenty of areas for improvement from the Bianconeri, whilst acknowledging that their opponents had made life difficult for them on Sunday.
Goals from Mauro Icardi and Ivan Perisic cancelled out Stephan Lichtsteiner's second-half opener to give Inter the much-needed win.
"Inter played well, but we failed to maintain our concentration tonight. We lost possession too easily and let them counter-attack too often. They did well to create chances, but as soon as we took the lead we needed to show that savvy in order to bring home the three points," he said.
Allegri reserved some praise to Miralem Pjanic's midfield display, the Bosnian deployed in the deep-lying role in place of the rested Mario Lemina.
"Pjanic was diligent in possession and effective in breaking up Inter's attacks. Lemina only started nine matches last season and I considered it too much of a risk to field him in so many matches in a row."
Juventus captain Gianluigi Buffon was quick to dispel suggestions that the Turin giants had taken Inter lightly.
"We didn't underestimate them, but you have to prove yourself on the pitch regardless of what's being said on the outside. For example, against Sassuolo people were lauding our display but I couldn't understand how we'd given them four clear chances at home — that can't happen."
"Despite the criticism we received after the Sevilla game, I thought we played well and looked solid, creating chances and not giving much away. Having said all that, this is only the start of the season and some ups and downs are to be expected: this defeat will do us good."
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