Sanchez laid on two goals as Jose Mourinho's side eased to a 4-0 FA Cup win at Yeovil Town, including a reverse pass for Herrera to thrash in United's second.
However, it was another aspect of the former Arsenal favourite's game that caught the eye of his new team-mate.
Asked for his thoughts on Sanchez's display by MUTV, Herrera said: "Yeah, amazing. He has played very good, but what I really like from him is the way he fights when he loses the ball.
"He is always ready to be the first defender of the team. That's going to be very important for us.
"Of course, we know his quality. He is going to be amazing for us but the way his first, the way he defends I really like it."
Sanchez is in line to make his Premier League debut for United when they travel to face Tottenham at Wembley next Wednesday.
He will also be available when the Red Devils return to Champions League action at the last-16 stage against Sevilla.
That competition provides Jose Mourinho's side with another possible route to silverware, with Herrera eager to point out that every trophy up for grabs will be fought for.
The Spanish midfielder added: "We have won the FA Cup two seasons ago and last season we won three trophies, so this club is about titles, and we are not going to give any competition away, we are going to fight for everything.
“Jesse Lingard [scored] again, Romelu [Lukaku] is also doing well this season and Juan Mata also has that quality to be in the right place in the box," said Ander.
"Alexis, we know, will score a lot of goals and we can add some goals from the midfield through [Marouane] Fellaini, Paul [Pogba] and [Nemanja] Matic who has a very good shot, as does Michael Carrick.
"I think we can be optimistic for the rest of the season. But we must know in the Premier League every team can beat you if you sleep for just one second so we have to be ready for the next game against Tottenham on Wednesday.”