Speaking to Sassuolo's official channels, the Scottish forward said his side had already shown they could find the net, but needed to translate that into a more consistent habit of taking and holding leads.
"We have to avoid any form of presumption," Bowie said. "We've shown we're capable of scoring, now we have to try to go ahead and hold onto it."
Bowie, a Scotland international who joined Sassuolo for around €10.5 million this summer after helping Hellas Verona to a strong second half of last season despite their relegation, was also asked about the Neroverdi's ambitions for the campaign, and was careful not to set any fixed target.
"We haven't set a precise goal," he said. "We have to keep trying to win game after game. The sky's the limit — we have to keep playing the way we are, improve, score and defend well. Then who knows what can happen."
The forward's measured tone reflects a club still finding its feet back in Serie A after promotion, aware that early results can flatter a squad that has yet to be fully tested against the division's strongest sides.
Sassuolo have shown attacking promise in the opening weeks of the season, with goals coming at a reasonable rate, but Bowie's comments suggest the dressing room is more focused on defensive solidity and match management than on any grander statement of intent.
Bowie arrived in Italy via Hibernian, having come through the academies of Raith Rovers and Fulham before a spell at Northampton Town, and made an immediate impression at Verona with four goals in his first half-season in Serie A.
That form persuaded Sassuolo to move for him even after Verona's relegation, seeing off interest from elsewhere in the division to complete the signing.