Man United should have had a penalty within the first four minutes of the game when Ciaran Clark brought down Wayne Rooney in the box but referee Roger East waved away their protests.
Villa frustrated United from then on but Herrera eventually broke the deadlock just before half time with a neat finish.
The Spaniard, who sealed the three points late on with another strike, praised United’s patient build-up play and insisted that they deserved the win.
Speaking about the game, Herrera said: “Aston Villa are fighting relegation and have to fight hard, so that made it difficult for us. They came to Old Trafford to wait and try to give us few opportunities.
“We kept the ball and tried to win the game through possession and being patient. That’s what we did.”
The cutting edge shown by United was a far cry to earlier in the season, where stagnant passes around the edge of the box characterised much of their play.
Louis van Gaal’s side have really pushed on in recent weeks and look more and more dangerous with each passing game. Herrera has played a key part in that and was instrumental in the victory against Villa at Old Trafford.