Mauricio Pellegrino was unable to guarantee Virgil van Dijk will stay at Southampton after leaving the Holland defender on the substitutes' bench for Saturday's 1-0 loss at Chelsea.
Marcos Alonso's free-kick was decisive as Saints' winless run was extended to five games to keep them in a congested lower half of the Premier League table.
Van Dijk was one of six changes to the line-up which had begun the midweek mauling by Leicester and his omission at Stamford Bridge sparked suggestions of a January departure.
Pellegrino insisted the former Celtic defender remained a key member of the squad after he started the previous 11 games, but would not rule out a move when the winter transfer window opens next month.
"Virgil is an important player," Pellegrino said.
"I can't control the market. I'm not the owner of the player. I can have my opinion and this I have give to the technical director, to the chairman, my opinion.
"After the board can decide altogether which is the best for the team."
Saints insisted last summer Van Dijk would not be sold despite a dalliance with Liverpool, while Manchester City and Chelsea have also been linked with a bid in the region of £70million.
Asked if Saints' resolve remained, Pellegrino added: "I can't control this. I will recommend to try to keep our best player here in the club. The club was clear in the beginning and I have the same opinion."
Van Dijk previously hinted at a move in October. Speaking to the Fox Sports in the Netherlands, he said:
"Of course, I wanted to make a step up, but Southampton did not want to sell me, but you're a professional, so now I will give everything to the club.
"Halfway through the season, maybe we can see what is possible."
Chelsea boss Antonio Conte expressed his admiration for Van Dijk after the game on Saturday.
Conte said: "He's a really good player. He had a bad (knee) injury, but I think he recovered very well. I wish him the best."
Chelsea have now won eight of their last 10 league matches, including five in a row at Stamford Bridge.
He suggested Chelsea deserve more credit for their form.
"I want to remember that in the last 10 games, we won eight games, drew only one game against Liverpool away and lost only one game, at West Ham," Conte added.
"If someone asks me if I want to sign for this in the next 10 games, I'm ready.
"Someone is forgetting this run, because there is a team (leaders Manchester City) winning every game."
Conte, sent off against Swansea and fined £8,000 for misconduct, had been complaining about Saints' persistent fouling and time-wasting in the first half.
But the Blues benefited on this occasion as more than the advertised minimum two minutes of first-half stoppage time had elapsed when Alonso curled in.
Conte suggested the officials had listened to and addressed his concerns since his expulsion.
He said: "I saw in the next game they tried to change the situation.
"It's important to protect the game, to pay attention to wasting time.
"I think sometimes to book the goalkeeper early it's very important. The game is faster."
Fraser Forster was not cautioned, but Alonso was booked for time-wasting at the end of the game. He will miss Wednesday's Carabao Cup quarter-final with Bournemouth for a fifth booking of the season.
Conte rued missed opportunities which meant Chelsea's lead was a fragile one.
He added: "This season we've created many chances, but we must be more accurate with the finishing. When you score more than one goal, you can stay more relaxed."