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With Everton leading 3-0, large sections of the home support left Villa Park in the 74th minute in protest against owner Randy Lerner and missed Rudy Gestede's 79th minute consolation goal for the league's bottom club.
The walk out followed criticism last week from former owner Doug Ellis, who said the club would be relegated and that Lerner had not invested enough time with the 1982 European Cup winners.
"It's always better when everyone - the fans, the club, players and manager - stick together," Garde told Sky Sports.
"When you are bottom of the league it is because there are problems and the more problems you have the more problems come as well.
"I don't want to make comments about that (protest), I've got enough work to do with the players in trying to give them the best solution to win the next game."
Seven-time English champions Villa, who are away to Manchester City on Saturday, have won only three of 28 league games and are eight points adrift of safety with 10 matches remaining.
