Mourinho brought Costa to Chelsea from Atletico Madrid in 2014 and the Spain global repaid that faith by firing the Blues to the Premier League crown in his first season in England's top flight.
Carrick, 35, is reluctant to make comparisons with Antonio Conte's leaders but is clearly frustrated that United - who have actually lost fewer games than the leaders - have seen their title hopes evaporate on the back of nine home draws.
'We must have good defensive organisation, and we must pay attention because, when he attacks the box, he's very risky.
"First of all, some guys are fresh, some guys are exhausted", the United boss said when asked how the sides compare.
The Portuguese has spoken of the difficulty of challenging for a top-four finish while advancing in the Europa League but Conte believes top teams can sustain challenges on more than one front.
"There is nothing I can do (about the current defensive situation)", said Mourinho. No different for me. But their run-in appears particularly tough, also featuring games at Arsenal and Tottenham Hotspur.
Chelsea's two wins over United in the league and FA Cup this season have been testy affairs, with Mourinho respectively rowing with Conte on the touchline and drawing the ire of the Stamford Bridge faithful. In 12 meetings since, Chelsea has won seven and drawn five.
It's the return match on Sunday, this time at Old Trafford.
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Mourinho's first return to Stamford Bridge since he was sacked at the end of 2015 saw United thrashed 4-0 in October its heaviest league defeat since 2011.
"I wanted to come to Chelsea because of Mourinho".
United opened the scoring in the 36th minute but failed to add to their tally and were left to rue their missed chances when Anderlecht made it 1-1 in the 86th minute with their only shot on target.
Mourinho said: "They have a certain style of play, they stick to it, they do it very well".
However, Chelsea has not kept a clean sheet in the Premier League for nine matches.
Though United's long sequence without defeat has not vaulted them into title contention, due to too many draws, Ibrahimovic's performances have been consistently excellent, helping him net 17 goals already in his first season in England.
"Zlatan is in the top form of his career", Conte said.
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