Marco Silva confirmed Mark Clattenburg apologised for allowing Alexis Sanchez's opener in the 2-0 defeat at Arsenal but Hull City's head coach insisted Kieran Gibbs should have been sent off.
Sanchez sealed the points for Arsenal in stoppage time from the penalty spot after Sam Clucas was dismissed for blocking a header by substitute Lucas Perez on the line with his elbow.
Handball claims also surrounded the Chile international's 34th-minute opener and, having reviewed replays of the incident at the interval, Clattenburg told Hull's players he erred for allowing the goal to stand after Arsenal's top scorer bundled home via his raised right arm.
Nevertheless, Silva had further cause for displeasure in the 54th minute when Gibbs barged Lazar Markovic to the floor when the on-loan Liverpool man seemed set to bear down on the Arsenal goal.
Asked whether the left-back should have seen red, the former Olympiacos boss told Sky Sports: "Yes. It is true. I don't want to talk about all the situations of the referee but Markovic goes to the goal, one against one with the keeper.
"Maybe it is one more important decision during the game but we need to do our job and that is not our job."
On the Sanchez incident, he said: "Arsenal were the better team in the first half but it is true they scored a goal with handball.
"At the start of the second half the referee apologised to my players. Okay, it is not good for us but we make mistakes and sometimes the referees make the same."
34 | Ball pinballs around the area Robertson clears off the line to Sanchez who appears to put the ball in the net with his hand #ARSHUL-- Hull City (@HullCity) February 11, 2017
Hull remain in the bottom three but with further cause for optimism following their latest encouraging performance under Silva, concluding a run of games against Manchester United, Liverpool and Arsenal that yielded four points.
"It's not a good congratulations for me," he told BBC Match of the Day when receiving praise for his team's performance.
"The most important for us is the result. We controlled all the second half, it was a very good second half.
"They started better than us in the first half. With some counter-attacks we gave them some problems as well.
"We came and try to play. We tried to change the result because it is not good for us.
"It [Hull's form] is positive. In my mind it is always possible to do better and to take more points. We need now to rest our payers. We have 15 days to work and prepare the next match."