Manchester United manager Ole Gunnar Solskjaer told BBC Sport: "You are always delighted with three points. The performance was good and we created chances.
"It was maybe a little too open and we wasted chances. We tried to play the Hollywood pass instead of securing the first one and using the space that was there.
"We are happy with what we are doing. We have shown we have improved a lot in a year. We lost to Arsenal away last New Year's Day. We have improved immensely."
Aston Villa boss Dean Smith told BBC Sport: "I wasn't happy with the first half. We were miles off the levels where we have been. It felt like a testimonial pace then they deservedly had the lead at half-time. I told the players we needed to be upping our levels.
"We competed a lot better [in the second half], showed more quality and created chances. I'd take the second-half performance all day long. A dubious penalty has lost us the game.
"When you look at our performances and results, it shows we are very competitive in this league now, which is what we wanted it to be."