Leg-spinner Rashid has been selected in the 13-man squad to face India at Edgbaston this week despite his self-imposed exile from county cricket.
Rashid, who won the last of his ten Test caps in Chennai more than 18 months ago, currently only has a limited-overs contract with Yorkshire.
“Our disappointment is not that Adil has been picked for England, we wish him well and hopefully he will be successful,” Moxon told BBC Radio 5 Live’s Sportsweek programme.
“Our disappointment is more the lack of communication and consultation that we’ve had in the background to this decision, but it’s not just about Yorkshire.
“I’m the representative of the coaches and directors of cricket on the ECB cricket committee, so I speak for them in trying to get our views about the game and the challenges that we have across to the ECB.
“Although we have been affected directly in this case there are cases going on that the counties feel a little bit aggrieved that communication [from the ECB] is not as good as it should be.
“The counties want England to be successful. But at the same time England need to have a respect of dealing with us fairly as well because we provide players for them.”
Moxon said he was surprised when England national selector Ed Smith contacted him last Tuesday to tell him it was a “possibility” that Rashid could be chosen for the Edgbaston Test.
Andy Flower, the ECB’s acting director of cricket, confirmed Rashid’s selection the following day, leaving Yorkshire to cope with what Moxon believes is a “crazy situation”.
“I read Ed Smith’s comments that he first broached this with Adil at the one-day international at Trent Bridge, two weeks prior to him ringing me when effectively the decision had been made,” Moxon said.
“We’ve employed Adil in good faith to play white-ball cricket for us, and now we’re coming into the final stages of the T20 competition and he’s not available.
“So it’s a crazy situation. We’re employing him to play white-ball cricket and he can’t play that for us in important games because he’s playing red-ball cricket which he did not want to play.
“Ironically, when Adil told us in February that he was going to give up red-ball cricket I said to him he was under-valuing himself.
“I told him with the talent he’s got he should be playing for England in all formats of the game.”
Rashid responded to criticism of his England call-up by casting doubt on his future at Headingley.
The 30-year-old said he would have appreciated Yorkshire’s chief executive or head coach offering their congratulations “as opposed to being angry and upset for not playing red-ball cricket for them, even though I told them I would not be doing so”.
But Moxon sought to build bridges when asked if Rashid had played his last game for Yorkshire.
“I hope not,” he replied. “We’ll sit down with his agent and discuss the future going forward.
“Adil has certainly got value to us. The problem we’ve got now is we’ve been put in a difficult situation because we’ve obviously been thinking to our squad as regards to next year.
“We offered him a one-day contract for next year, but now Ed Smith is saying that every player who is going to play Test cricket has to have a red-ball contract.
“So we’ve got to work out how we’re going to square that circle and our plans for 2019 might change slightly now.
“That’s why I am disappointed in Ed Smith because he hasn’t thought through the consequences of this selection.”