Chelsea tried to re-sign their old striker Lukaku from Everton this year but the clubs could not agree on a fee with the Belgian now valued at more than the 28 million pounds Everton paid for him in 2014.
Lukaku, 23, has scored seven goals this season for the Merseysiders and offers the main threat to Conte's in-form side when they meet at Stamford Bridge on Saturday.
Yet the Italian was in no mood to dwell on the one that got away as he chose to hail his Spanish striker Costa, the league's leading scorer with eight goals, as the "complete player".
"I regret for nothing," Conte told reporters on Friday.
"We have Diego who is playing fantastic football, not only scoring the goals but working a lot and very well for the team.
"I think that I'm seeing a complete player in Diego. It's fantastic for me, for the team, to have him in the team. He's scoring a lot but, above all, he's working a lot for the team. That's very important," he added.
"When we have our strikers, plus Eden Hazard, Pedro, Willian and Oscar all working so well for the team, it's fantastic.
"Lukaku is a very good player, young and improving a lot, but it's right to talk about my players. I'm very satisfied with my players. I hope Diego continues in this way because his commitment is incredible."
Chelsea, one point behind the league's leading trio of Manchester City, Arsenal and Liverpool, are in buoyant mood, seeking a fifth successive league win.
It is not just Costa who is flying for the Blues, though.
The rejuvenated Eden Hazard was voted the Professional Footballers' Association fans' player of the month this week.
Cesc Fabregas's position, though, remains uncertain amid media reports that the Spanish international, who has been injured, would be sent out on loan in January transfer window.
"We are at the start of November... For this type of situation it is too early to talk. Fabregas is Chelsea's player and I'm very happy to have him in my squad," Conte said.
(Reporting by Ian Chadband, editing by Ed Osmond)
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