United are languishing in 14th place on eight points with two wins from nine games in all competitions and Sunday's match was clouded by media speculation about Ten Hag's future.
The club's senior leadership team -- co-owner Jim Ratcliffe, CEO Omar Berrada, sporting director Dan Ashworth and technical director Jason Wilcox -- watched on intently at Villa Park.
"We are all on board together, on one page, we know what we are working through it's a long-term process," Ten Hag said. "We have come through two very tough away games (including Thursday's 3-3 Europa League draw at Porto).
"This is a team, we showed the belief and faith we have."
A victory might have eased the pressure on Ten Hag, and captain Bruno Fernandes nearly earned one when his long-range free kick hit the bar in the second half. Marcus Rashford also forced Villa keeper Emi Martinez to make two excellent saves.
"We created loads of chances in our seven (Premier League) games but we have to step up," Ten Hag said.
"We have to take into consideration (striker Rasmus) Hojlund is returning, he's still coming up to full fitness. But others are stepping up. I was impressed by Rashford, also (Alejandro) Garnacho is so good and Antony at the end."
Ten Hag headed over to United's travelling fans after what must have felt like a victory to applaud their support while Duran Duran's "Hungry Like a Wolf" played on the loudspeakers.
United defender Jonny Evans noted the talk about Ten Hag's future affected the players, saying: "It's on our minds too."
While the Premier League does not resume until Oct. 19 due to the international break, the scrutiny on Ten Hag will likely not diminish, with United's hierarchy set to hold their monthly meeting in London on Tuesday.
Ratcliffe said on Friday that the decision on Ten Hag's future is not his to make.
