Hawk-Eye says a “technical error led to an incorrect graphic being provided”.
Mata said “the decision was not very clear”, while United boss Jose Mourinho called for the video assistant referee (VAR) system to be made “perfect”.
The system is being trialled in the FA Cup and Carabao Cup this season.
It was praised after correctly overturning a decision to rule out Kelechi Iheanacho’s strike for Leicester in their 2-0 FA Cup third-round replay winover Fleetwood in January.
However, it was also described as a “shambles” by former England captain Alan Shearer after the system’s use failed to result in a penalty for Chelsea during their FA Cup replay with Norwich.
On Saturday, Mata appeared to have put Manchester United 2-0 up just before the break when he ran on to Ashley Young’s neat pass – but while the visiting team was celebrating, referee Kevin Friend listened to his earpiece for the VAR input.
After a wait of around a minute, the goal was ruled out for offside, with viewers watching the match live on BT Sport then presented with the faulty graphic.
Hawk-Eye’s statement read: “A technical error led to an incorrect graphic being provided by Hawkeye to BT Sport on Saturday.
“To confirm, the VAR saw the correct image with the correct lines to make the decision. This was a case of the wrong image being provided to the broadcaster and we apologise.”