Chilwell was a second-half substitute at the Vitality Stadium but failed to substantially alter the team’s fortunes as they laboured in vain to break the hosts down in wet conditions.
Pochettino named three outfield players aged 19 or under on the bench as well as two goalkeepers as the club’s injury crisis continued to deepen.
Marc Cucurella and Noni Madueke were fresh additions to the absentee list at Bournemouth, taking the total number of players unavailable to the manager to 12.
Chelsea threatened only sporadically, looking to use the channels to attack but only rarely finding a final ball to open up the home side.
Raheem Sterling hit the crossbar with a fiercely hit free-kick whilst Nicolas Jackson also struck the woodwork in the first half but it was Robert Sanchez who was called upon to make the save of the game when he spread himself low at the feet of Dango Ouattara as the striker bore down on his goal.
It leaves Pochettino’s side 14th in the table with just one win from five matches, and with an uneasy sense that last season’s problems in front of goal are a long way from being fixed.
And some fans seemed to vent their frustrations when England international Chilwell went over to applaud the away end at full-time.
“What can we do?” said Pochettino. “For me, I have nothing to say. The fans can do whatever they want.
“We know what we need to do, we are strong in our belief. We have 12 injured and today we had three or four young guys and two keepers on the bench.
“I’m going to cry? I’m going to complain? To who? I need to accept this, the challenge and keep being positive.”
The Argentinian continued: “Bournemouth is a good team, they are going to compete. Every team is going to compete and be difficult.
“But these are the circumstances we need to accept and be positive, patient. We are not going to change in the way we do things.
“What can I do? Only to keep believing. If you say to me we have today all of our players, all of our signings, no injuries, and maybe we cannot win this game? Then maybe I can tell you we need to see (it) in a different way. But we cannot lie to the people.”
Chelsea have failed to score in their last two Premier League outings and have won just twice in the league since March, at the Vitality Stadium late last season when Bournemouth were already safe and last month at home to newly-promoted Luton.
Pochettino was asked whether he was sympathetic to the reaction of those supporters that booed the players off.
“What I can tell the fans is the circumstance that we cannot change,” he said. “The reality that we cannot change. We have too many players (injured). We’re a team that would be strong if we are together.
“Even Manchester City, Arsenal, when they have all the squad fit, they can compete for everything. Why is it different for us? It’s because of what? We don’t have all the squad available from the beginning of the season.”
Bournemouth boss Andoni Iraola reflected on a performance that showed promise despite the winless run at the start of his tenure now stretching to five league matches.
“I’m really happy with the performance,” he said. “The game was quite level. Both teams had their chances. Overall, we had very good individual performances and finished the game even better.
“There were moments later on where we thought the game could be ours.”