The Toffees have not won since September and are at home to rivals Liverpool on Wednesday
Bees striker Ivan Toney scored the only goal of the game from the penalty spot in the 24th minute after Andros Townsend had caught Frank Onyeka with a high foot inside the area.
The Toffees were poor during the first half and while they improved after the break, Brentford goalkeeper Alvaro Fernandez was rarely called into action.
The Everton fans made their feelings known at full-time, with some angry reactions when the players went over to applaud the travelling faithful.
“We can understand the frustration of the fans but we are also frustrated,” Benitez said after watching his team lose for the fifth time in six matches.
“Today you cannot complain about the effort and intensity the players put in. They try until the end, we had a lot of crosses and shots, so you cannot complain about the effort but you can be disappointed because obviously we do not want to lose.”
Everton’s run without a win stretches back to 25 September. Injuries have hampered their cause with Dominic Calvert-Lewin and Abdoulaye Doucoure among several to be absent for the majority of that period, although the latter did return to start at Brentford.
Richarlison was also suspended for the fixture in the capital but will return for Wednesday’s crunch clash at home to Merseyside rivals Liverpool
The summer appointment of Benitez was met with criticism due to his history with the Reds, but the Spaniard made a good start to life at Goodison Park and won four of his opening six league games. He is positive they can get back to that type of form, with the club currently languishing in 14th position.
“We didn’t deserve to lose but the reality is the team is giving everything on the pitch and you can see the togetherness of the players,” the 61-year-old said.
“If we consider what we did at the beginning of the season, we saw enough quality to know we can be doing much better.
“But even the games we draw [against Manchester United and Tottenham], the team was doing enough to get more from these games.
“It is a question of confidence, missing players but you could see what we were capable of doing at the beginning of the season. When we have everyone available, I am confident we will do it again.”
Thomas Frank’s Brentford had not tasted victory in the Premier League since the start of October but were deservedly in front at half-time thanks to Toney’s fifth goal of the campaign and defended impressively after the break.
It helped the Bees return to winning ways at their home stadium, having not triumphed there in the top flight since the opening day of the season.
“We hadn’t won in five, we deserved more in those games and everyone knows it, but to get the win you need to defend well and we got back to top-level defending today,” Frank said.
“And finally we got the home win we have been searching for and fighting very hard to get. It was a fantastic atmosphere and especially at the end, so for many reasons it was a vital win.”