Alex Iwobi scored deep in stoppage time as Fulham shocked a sub-par United 2-1, the London side's first win at Old Trafford since 2003 and only their second in 61 years.
United had not lost in their five last league games, but the optimism that had been growing around Old Trafford was dented by Iwobi's 97th-minute goal.
"I said from January on we are (playing) finals, and we won many finals," Ten Hag told reporters. "Now we lost one final."
United are sixth in the table on 44 points after 26 games, while Villa, who beat Nottingham Forest 4-2 on Saturday, have 52.
United's loss came three days after new co-owner Jim Ratcliffe vowed to knock arch-rivals Manchester City and Liverpool off their perch.
Ten Hag said the future remained positive, pointing out that the team has been hard-hit by injuries with striker Rasmus Hojlund, who had scored in United's six previous league games, and defender Luke Shaw the latest absentees.
"You have to see the bigger picture and the bigger picture looks very good," Ten Hag said. "We have to catch up in certain positions, get the injuries back, because then we will be more in balance.
"We are going in the right direction. And when we have the players of the squad available, we have a very good team."
