Chelsea are top of the Premier League with four games to play and in the May 27 FA Cup final with Arsenal as Conte seeks the double in his first season as head coach.
But speculation continues to surround the future of players including Costa, who has again been linked with a mega-money move to Tianjin Quanjian, and Cesc Fabregas, who is not guaranteed a starting spot under Conte.
The Italian did not clarify Costa’s situation on Friday, saying: “The present is very important for us. Now is more important than the future.”
And when he was later asked if he could keep Fabregas happy, Conte outlined his preference.
“I like to underline a concept — that I mustn’t keep the players happy. We must win.
“You speak about ‘happy’. I speak about ‘to win’ and to work very hard.
“Players are not always happy to work very hard.
“But I think my target is to put in the mind of my players a winning mentality, and a winning mentality doesn’t have to keep the players happy. It’s very difficult to keep 20 players happy.
“I don’t want this. I want players ready to fight and to try to put themselves in the team, to try to win together.
“Then, if you are happy or unhappy, I don’t care.”
Costa was happy at the start of the season, scoring goals at ease, but he endured a seven-game scoreless streak which ended with a double in last month’s 4-2 win over Southampton.
The striker missed January’s trip to Leicester amid reports his head had been turned by a lucrative offer to join Tianjin in the Chinese Super League. Conte publicly insisted Costa’s absence was due to a back injury.
Reports resurfaced this week of a move being agreed, although Tianjin took to Weibo — China’s equivalent of Twitter — to deny any negotiations had taken place.
“I don’t know about this,” Conte said.
Costa has scored 19 goals this season and 51 in 86 Premier League appearances since signing from Atletico Madrid in July 2014.
However, he has two years left on his contract, is 29 in October and Chelsea may be prepared to sell and reinvest the funds, reportedly in the region of £76m, in the squad.
Everton striker Romelu Lukaku has been subject of speculation over a return to Chelsea, while this week also saw rumours over the futures of Willian and Fabregas, who turned 30 on Thursday.
Conte added: “Speculation or news, for me, is not important.
“The most important thing is for us to be focused.”
Conte refuses to underestimate Boro, with Spurs poised to pounce.
“It won’t be easy. Middlesbrough is struggling to avoid relegation.
“We must be ready, ready to fight, ready to find the right way to take three points.”