The Red Devils climbed back into the top four thanks to Rashford’s 15th Premier League goal – and 28th in all competitions for his club – this season.
“Yes, it’s the truth,” said Ten Hag when asked whether United were too reliant on Rashford.
“But we know other players can score as well. Bruno [Fernandes] can score as well. We have many more players across the squad who can score.”
Only Napoli’s Victor Osimhen has more league goals in Europe’s top five leagues since the World Cup than Rashford, who has scored 10 winners in the Premier League this season, the most by a Manchester United player in a campaign since Wayne Rooney in 2009-10.
His latest winner took United back above Tottenham in the race to qualify for the Champions League, and was the response Ten Hag needed following Sunday’s defeat at Newcastle.
Brentford, who are chasing European qualification, lost for only the second time in 17 Premier League matches.
Scott McTominay and Antony went close before Rashford finished from close range, with a headed assist by Marcel Sabitzer, after the Bees failed to deal properly with a corner.
Brentford, flat for large parts of the first half, were much better after half-time and United were relieved to hear the final whistle.
Home goalkeeper David de Gea needed treatment after making a crucial save to keep out substitute Kevin Schade.
United are level on 53 points with third-placed Newcastle – and three ahead of fifth-placed Tottenham, who have played one more game than their rivals.
Brentford stay ninth – three points behind sixth-placed Brighton, having played two more games than the Seagulls.
Nervy Man Utd secure the points
Manchester United had a eight-point cushion on fifth spot after defeating Leicester on 19 February but Sunday’s defeat – coupled with Tottenham’s draw at Everton on Monday – left them outside the top four for the first time since December.
Manager Ten Hag recalled Jadon Sancho in an attempt to provide the team with more energy yet United were hanging on towards the end against a Brentford side that grew in confidence.
Sabitzer tested David Raya after half-time while Fred blazed another opportunity over the bar but United were forced to endure several nervous moments before full-time after failing to add to their tally.
De Gea’s save from Schade was a huge moment in the game, the Spaniard keeping his composure to thwart the Brentford player who was clean through with only the keeper to beat.
Questions will remain about United’s over-reliance on Rashford for goals but Ten Hag will hope United will build on their first Premier League win since winning the Carabao Cup.
“It’s not acceptable what we did on Sunday,” added Ten Hag. “Today, that was the performance I expect and demand.”
Season to remember for Bees
Brentford have spent the past few months making a mockery of second-season syndrome.
Having finished 13th last season following promotion from the Championship, the Bees are just three points away from equalling last season’s tally of 46 points – which secured them 13th spot – despite defeat at Old Trafford.
They followed up their 4-0 thrashing of United in London on 13 August with statement wins over Manchester City and Liverpool and they so nearly came close to snatching a point here only for De Gea to produce the save of the game.
Thomas Frank’s side entertain in-form Newcastle – 5-1 winners at West Ham – next but it is a testimony to the efforts over the past eight months that they are still in with an outside chance of Europe at the business end of the season.
“It’s a good picture of how far we have come that we’re sitting here disappointed we’ve not got anything out of the game,” said Frank.
“We’re just disappointed that we didn’t get anything of it. That’s crazy because we were playing Manchester United. Sometimes we have to remind ourselves of who we are and what we have done.”