Simone Inzaghi was left frustrated as Inter failed to capitalise on their opportunities, needing to come from behind to earn a 1-1 draw with Monza.
Dany Mota gave Monza the lead in the 81st minute, while Denzel Dumfries spared the champions' blushes by netting the equaliser seven minutes later.
They were knocked off the Serie A summit after dropping points for the second time this season, with Napoli leapfrogging them to the top of the table.
"We had difficulties against a team that played a good defensive game," Inzaghi told a press conference. "We had chances that we didn't convert, we made technical mistakes.
"Then in the second half, we didn't do well, we didn't create dangerous situations, and when we switched to three [up front], we had this great goal from Dany Mota that created difficulties for us."
Inter intensified their efforts after going behind, but time was not on their side as they tried to wrap up three points. Overall, the visitors managed 16 shots but only got two of those on target in a wasteful performance.
"We had a great reaction after the goal, maybe we should have had it earlier," Inzaghi added.
"We had a couple of situations that weren't exactly clear, usually we manage to capitalize on them. In games like this, you have to try to unlock the result... If you stay tied and concede goals, games become difficult."
Argentine striker Lautaro Martinez had an early chance to put Inter in front but sent his header slightly above the bar.
Last season's Serie A top scorer, who finished the campaign with 24 goals, remains goalless in Serie A so far.
"He had a little problem, he couldn't train a lot," Inzaghi said.
"The attack was the only department where I had one player, [Joaquin] Correa, in the last 10 days [in training]. We thought we would find the goal sooner.
"The team was a bit slow but until [conceding] the goal [Yann] Sommer had no work. But you accept a goal like that more than the ones we conceded on the first match day, even tonight overall defensively we did well."
Inter drew 2-2 at Genoa in their season opener, before consecutive home wins against Lecce and Atalanta, in which they kept a clean sheet in both.
They get their Champions League campaign underway when they travel to Manchester City on Wednesday.
"I'm quite calm," Inzaghi assured. "I have all the players available, and this new Champions League is something new for all of us coaches.
"It's the first year [of the new format], there are two more games without the usual group. We'll have to try to do our best, any opponent we find in the Champions League is difficult."