Everton's board of directors were reportedly absent from the club's 1-0 win over Arsenal.
The directors previously missed the 2-1 home defeat to Southampton on January 14, after a club statement claimed that they had been advised against attending.
The board consists of chairman Bill Kenwright, CEO Denise Barrett-Baxendale, Chief Finance and Strategy Officer Grant Ingles and Non-Executive Director Graeme Sharp.
Everton have grown frustrated with the club's ownership under Farhad Moshiri and tensions only worsened following an unsuccessful transfer window.
The Toffees sold academy product Anthony Gordon for £40m to Newcastle United, and they were ultimately unable to strengthen their squad.
Despite being linked with several players, Everton ended the January transfer window without completing a single signing.
Everton supporters have staged a number of protests against Moshiri and the club's ownership, and their most recent demonstration took place around Goodison Park ahead of Saturday's Premier League meeting with Arsenal.
A banner was also flown over Goodson Park less than 10 minutes into the first half, which read: 'League's worst run club. #Time2GoBill'.
According to the Daily Mail, the board of directors were absent from Sean Dyche's first game in charge.
Previous advice which prevented the board from attending the Southampton game had not changed, and as a result, they missed the victory over Arsenal on security grounds.
On the pitch, Everton enjoyed a successful afternoon, claiming a narrow 1-0 victory over the Premier League leaders.
James Tarkowski headed home the winning goal from a corner, ensuring that Dyche's first managerial job since leaving Burnley in April last year got off to a perfect start.
Despite claiming their first Premier League victory since October 22, Everton remain in the relegation zone on goal difference.
Next up for the Toffees is a derby meeting with their local rivals Liverpool at Anfield.
