The newspaper's front page previewed Inter's Friday night clash against Roma with a photo of both Lukaku and Smalling above the headline "Black Friday."
Lukaku released a statement calling it "one of the most dumbest headlines I have ever seen in my career."
The Belgium international continued saying: "You guys keep fuelling the negativity and [racism] issue instead of talking about the beautiful game that's going to played at San Siro between two great clubs... education is key."
Lukaku has been the subject of racist abuse in Serie A this season, with Cagliari supporters having aimed monkey chants at him when the sides met in September. He joined Inter for €80 million from Manchester United while his former Old Trafford teammate Smalling moved to Roma on loan.
Smalling said: "Whilst I would have like to spend the day focusing on the big game tomorrow, it is important I acknowledge that what occurred this morning was wrong and highly insensitive.
"I hope the editors involved in running this headline take full responsibility and understand the power they possess through words, and the power those words can have."
Both Inter and Roma released a joint statement later Thursday saying they would ban Corriere from their training facilities for the rest of the year.
"Roma and Milan have decided to ban Corriere dello Sport from our training facilities for the rest of the year and our players will not carry out any media activities with the newspaper during this period.
"Both clubs are aware that the actual newspaper article associated with the 'BLACK FRIDAY' headline did portray an anti-racist message and for this reason, we have only banned Corriere dello Sport until January."
Inter had earlier tweeted: "Football is passion, culture and brotherhood. We are and always will be opposed to any form of discrimination."
Sources have told ESPN the post was in relation to Corriere's front page, but the club opted not to directly reference it in the tweet as not to "give it visibility."
Roma's English account also had tweeted a picture of the front page as part of their condemnation, and Fiorentina's English Twitter account responded by writing, "No to racism, kick it out" -- as well as a separate post criticising the cover.
AC Milan also condemned the cover with a tweet that read, "It is totally unacceptable to see such casual ignorance on racism. We will not stay silent on this issue."
The newspaper released a defence of their front page in a statement titled, "The Eulogy of Difference."
In it, they wrote: "Denying the diversity is the typical racist, macroscopic, stumbling block of the anti-racists. The mental slum of Sunday's moralists when even Thursday is Sunday. 'Black Friday,' for who wants to understand it, was just a eulogy of diversity, the pride of diversity, the magnificent richness of diversity.
"If you don't understand it, it's because you can't or you pretend not to."
Asked about the headline, Roma boss Paulo Fonseca said: "I don't think it's a good choice of words. We need to be more aware when we talk about issues related to racism -- we need to be more considerate."
Lukaku's agent, Federico Pastorello, criticised the front page in an interview with Sky Sports, saying, "Being Italian, I'm really ashamed to read a title like that, but I really don't want to talk about a single episode.
"At the end of the day, the racist problem is a big problem. Unfortunately we are living in 1920. It's really a culture problem."
All 20 Serie A clubs signed an open letter last week, acknowledging that racism is a serious problem in Italy and requested help in order to deal with it.