"We are extremely disappointed and strongly condemn this image showing some of our players with family and friends together at Christmas," a Tottenham statement read.
"Particularly as we know the sacrifices everybody around the country made to stay safe over the festive period.
"The rules are clear, there are no exceptions, and we regularly remind all our players and staff about the latest protocols and their responsibilities to adhere and set an example.
"The matter will be dealt with internally."
Lamela and Lo Celso are not involved in Spurs' Saturday clash with Leeds United, while Reguilon is on the bench.
"I gave [it to] him because I was told he was going to spend Christmas on his own. I had this thought about him. He was not alone as you could see and we as a club of course feel disappointed because we give the players all the education, we give the players all the conditions and of course we are not happy.
"It was a negative surprise for us.
"I prefer to say disappointed [rather than angry]. We know what we are internally. We don't need to open the door to you and let you know what is going on internally, what are going to be the consequences, how deeply we approach that negative surprise. I feel disappointed, just that."
"I don't want to speak too much about it," Mourinho told reporters ahead of Saturday's match against Leeds United. Just to say I felt [it was] unprofessional, but that is the way it was.
"We were preparing ourselves for that match and of course we didn't play, and that is disruptive of what is a week of work.
"Training sessions before that would be different if we were going to play that game. People say good for me that there was no game, but only good for me if I knew there was no game."
West Ham said: "The club has set the highest possible standards with its protocols and measures relating to COVID-19 so we are disappointed to learn of Manuel Lanzini's actions.
"The matter has been dealt with internally and Manuel has been strongly reminded of his responsibilities."