Deila has been critical of the United duo: Connolly for what he perceived to be a blatant dive in their Scottish Cup quarter-final draw at Tannadice to win a penalty and McGowan for what he claimed to be a career-threatening tackle on Liam Henderson.
The United boss, who is preparing his side for a fourth successive clash against the Hoops, says those comments are telling.
“I don’t agree with Deila,” he told STV with regards to McGowan’s tackle.
“Ronny’s comments are very wrong. From the first game his comments on young Aidan Connolly for his diving.
“I understand Ronny is under a lot of pressure because of what happened at the start of the season and what is expected of Celtic to win the treble.
“The money they’ve spent and taking a couple of our players in January – he’s under enormous pressure.”