Rashford laid on Antony's fourth minute opener, then played in the cross that forced Conor Coady into an own goal early in the second half, before making it seven straight home games with a goal for United as he scored a stoppage time penalty.
"From the first minute I think Marcus was the one who showed the confidence and the belief," Ten Hag said. "He was taking on players and I think for 90 minutes he was a threat to the Everton defence."
Rashford is now up to 13 goals for the season, on course to beat his previous best tally of 22, achieved in 2019-20, if he can stay fit.
"In football it is hard to measure but with a striker you measure goals and assists - today he has two assists and one goal," Ten Hag added. "He has fantastic skills and when he has mental stability he can keep going.
"That demands a lot from us as a team and an organisation to make sure we have the right environment and culture. When he keeps focus like this for sure he can keep this going…
"As a team we have to make sure we create the space, playing to his strengths. That is about Marcus doing really well but also the team, getting into the shapes. I think he is unstoppable with his speed, his dribbles and his directness."
United can now look forward to Sunday's fourth round draw, but perhaps more importantly have kept their winning run - now up to seven games ahead of Tuesday's Carabao Cup fixture against Charlton - going as Premier League fixtures against Manchester City and Arsenal loom later this month.
"I think we have good belief," Ten Hag said. "We have to keep the freshness with so many games. I think with one or two players we could see the load was high, we have to make sure we get the right balance with load and relaxation for the players.
"The games keep coming and this is a good challenge. When we face the big games like City and Arsenal the physical performance has to be top."
Although relegation-threatened Everton endured an eighth game without a win, under-pressure Frank Lampard was encouraged by the way his players responded to their capitulation in Tuesday's 4-1 home defeat to Brighton in the Premier League.
"The performance was on a similar level and possibly better in an attacking sense than at Manchester City (last weekend)," he said. "We got a draw at City and I think we deserved a draw today.
"I was really pleased with the spirit and the bravery of the team. We didn't get the result, that's sometimes how football goes. When you've got an individual of Rashford's quality they have their moments."
Although the 9,000 travelling Everton fans frequently chanted "sack the board", they did not turn on the players or the manager at Old Trafford, and stayed behind to applaud their efforts in defeat.
"I think the reaction at the end of the game spells it out," Lampard said. "They saw the spirit in the team, the way we play and I think they saw we deserved to get a draw."
Everton had looked shaky early on, but after Coady cancelled out Antony's opener in the 14th minute they battled well.
But a nasty looking injury for Alex Iwobi - who went off on a stretcher early in the second half - came just before United retook the lead.
"It's an ankle ligament injury," Lampard said. "We're hoping it's a lesser one but I don't know the extent of it. He left on crutches."