Speaking to BT Sport after his side's dramatic 3-2 win over Brighton, Solskjaer joked it was lucky that the Spurs boss wasn't there to measure the goals.
"Last season we had too many draws, so that is a big plus for us," he said. "You have to be happy Jose is not here to measure the goalposts."
Mourinho responded to Solskjaer on Sunday before his side's game against Newcastle United.
"I think Ole yes was so happy and surprised with what happened to his team that he had a joke," he said.
"I understand that for him the dimensions of the goalposts are not important for him. What is important for him are the dimensions of the 18-yard box.
"He would never accept to play with a 17-yard box. I think he would prefer a 22-yard box. For him it would be better."
United were awarded a penalty after the final whistle had blown in their game against Brighton on Saturday after Neal Maupay was judged to have handled a Harry Maguire header in the box in the 100th minute of the match.
The former United manager had previously joked about the side's penalty record, saying it is unsurprising Bruno Fernandes is good at penalties as he "had about 20 to score" during the 2019-20 season.