Jose Callejon's goal on the cusp of half-time was enough to earn Napoli a second Serie A victory over Inter this season, and Pioli's side are now without a win in their last six matches.
Supporters at San Siro displayed banners and voiced their dissatisfaction with Inter's downturn in form in recent weeks, but Pioli called for patience to allow Chinese owners Suning Holdings Group, who became the club's majority shareholders in 2016, to make the team competitive again.
"We are at the start of a new era," he told Mediaset Premium. "There are new club directors, new objectives, but we are laying the foundations to build something important here at Inter.
"We need to make the right choices going forward. I don't think we lacked a strategy or identity tonight at all. We had ideas, but weren't precise enough to make them work. This was different to recent games and we had difficulty against a very strong opponent.
"Napoli are a very strong side, they proved that again tonight, but we needed to be more precise and not make a serious error right before half-time."
Club owner Zhang Jindong publicly announced his support for Pioli in the build-up to the game and the coach, who led Inter on a nine-match winning streak in December and January, said that catching rivals AC Milan was not impossible in the last four games of the season.
Sixth-placed Milan are three points ahead of Inter, and Pioli said: "We have run out of steam a little bit, but Milan aren't that far away and we'll try to win the next four games.
"I have always felt the faith and support of the club. We're working on a process. Recent results have been poor and we lacked a bit of quality, but Napoli also forced us to play outside our comfort zone by pressing all over the park."
Napoli coach Maurizio Sarri reflected on points dropped earlier in the season after his side broke the club record for away wins in a single campaign with their 11th victory on the road.
Sarri's men are third in the table, one point behind second-placed Roma, but he said: "We have the feeling of having thrown away a few points in a stupid way. If Roma win all their games then we cannot recover.
"We have salaries that are not even half those of other teams. We are the dreamers of the division."