Quins rugby director Conor O'Shea was angry over what he considered to be Davey's poor work at the breakdown while Exeter head coach Rob Baxter expressed his frustration at losing 19-13 despite a compelling superiority in the scrum, in possession and territory.
"We had to dig in out there, and to come back as we did and score 10 quick points after falling behind speaks volumes for the attitude of the players," said O'Shea.
"It was not the prettiest of games because there was a lack of tempo, but then we realise that teams will come here to stop us playing.
"For us, the breakdown was an absolute nightmare. Players not rolling away after tackling, players going over the top. It can only be a matter of a second lost, but in rugby those seconds are priceless and can cost you an attacking opportunity.
"We needed to get to the breakdown in numbers and will be working on that during the week."
O'Shea was careful not to mention the referee specifically, but his inference was clear - Exeter were not being refereed correctly in his opinion.
He added: "We will not play brilliant rugby every week, but we did not get frustrated when things were clearly not going right for us at the breakdown.
"They are a bloody good side, well coached, well structured and destined for a top-four finish while we will play better this season and lose, but you do need areas to function if you are to get tempo in your game."
Baxter was so annoyed at the whistle that he walked on to the field and expressed his disappointment personally to Davey.
"I spoke with the referee and told him that I felt there were inaccuracies in the game that I shall look at further during the week before making my report." Baxter said.
"Frankly, I am not happy with the way the game was officiated.
"I am massively frustrated. Not with our guys because they did everything asked of them. But there are certain elements of a rugby game over which you have no control.
"When you add up territory, possession and chances created, you tend to earn some reward in terms of decisions. But we didn't.
"I admit, however, that we also had good scoring opportunities which we did not take, one early on that should have earned us a try.
"But we have proved again that we are a good side in only our second season in the Premiership. We came away with a bonus point, which is more than we took home from here last season."
Nick Evans came to the rescue of his team with another immaculate kicking display comprising four penalties and converting a Mike Brown try.
Bryan Rennie scored Exeter's try, converted by Ignacio Mieres who also kicked two goals.
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