Mourinho's comments were in response to a Facebook post from the Gunners' official account, which poked fun at Tottenham's 3-1 defeat at Sheffield United on Thursday.
The morning after the game, Arsenal posted a highlights video of their 2-1 win over the Blades last month with the caption, 'It's not easy beating Sheffield United at Bramall Lane. Here's a reminder of how it's done' and accompanied by the eyes and wink emojis.
"I think if they were top of the League or fighting for top four in a really good moment they wouldn't enjoy the problems of others," responded Mourinho.
"You only enjoy the problems of others when you are also in trouble. In the end it says more about them, they don't have much to celebrate [so] they have to get every opportunity to do it. They are in a very similar situation to us in the table.
"I don't like to connect the club with some post or tweet," the Spurs manager added.
"Maybe I am wrong, maybe I am right, but the person that did it probably did by themselves.
"I don't believe that was [Arsenal boss Mikel] Arteta that posted, I don't believe it was [Granit] Xhaka or another captain that did it. It was probably some guy that was at home for three months working from home. No problem at home, but we will be waiting for them [on Sunday]."