A reported bust-up with Antonio Conte and his staff, as well as speculation over a move to the Chinese Super League, had little impact on Costa in Sunday's 2-0 win over Hull.
The 28-year-old striker scored his 52nd Chelsea goal on his 100th appearance and celebrated by gesturing about all the noise which has surrounded him since missing the win at Leicester, officially due to a back injury.
Former Barcelona forward Pedro said: "He is perfect for this team.
"I have played with important people, important players like (Zlatan) Ibrahimovic (at Barcelona).
"But Costa is a very good striker too, a very good runner, strong physically and scores more goals for the team."
Cesc Fabregas says Costa is integral to Chelsea's bid to win the Premier League title.
"We need him if we want to achieve our targets," Fabregas said.
"It was a good goal and he's always there when we need him.
"We know what Diego brings to the team, nothing needs to be said about that
We're pleased he's back."
Costa's goalscoring return concluded a near-ideal weekend for Chelsea, who lead the standings by eight points.
Rivals Liverpool, Manchester City, Tottenham and Manchester United dropped points on Saturday, while Arsenal narrowly avoided doing so on Sunday.
Chelsea's next Premier League games - following Saturday's FA Cup fourth-round tie with neighbours Brentford - are at Liverpool on January 31 and at home to Arsenal on February 4.
Chelsea lost the reverse fixtures earlier this season before embarking on a 13-match winning run.
Goalkeeper Thibaut Courtois says the Blues' winning mentality and dominant position in the table is now dispiriting for their rivals.
Courtois told Chelsea TV: "We win our games and then it's really hard for other teams to see that the team that's top of the table still keeps winning games
That really sends a message.
"But we have to keep going
Next week we have the FA Cup, then we play Liverpool and Arsenal in the same week.
"It will be a hard week and we hope to have the maximum points."
Courtois made a number of saves against Hull as he recorded a 13th Premier League clean sheet of the season.
"If we keep clean sheets we can win our games and that's the most important (thing)," the Belgium goalkeeper added.
Hull play Manchester United in Thursday's EFL Cup semi-final second leg on Thursday and Fulham in the FA Cup on Sunday before returning their focus to the league.
February's opponents are United, Liverpool, Arsenal and Burnley, but defender Harry Maguire says City can take confidence from the performance at Stamford Bridge.
"We've got a benchmark now," Maguire told Hull's official website.
"The last couple of games we feel like we've performed better.
"We won't by lying down and giving in to any top-four teams
We'll be going there to try to get the win.
"When we're on top in games we need to start creating more chances and taking them."
Maguire did bemoan the decision early in the second half not to award Hull a penalty for Marcos Alonso's challenge on Abel Hernandez.
Maguire added: "Big decisions didn't go our way
We've got to take it on the chin now and go into the next few games with plenty of positives to take."
Source : PA