Solskjaer believes his men have improved a lot within a year, citing an example with United’s defeat against Arsenal at the Emirates Stadium on January 1, 2020.
Anthony Martial gave the hosts the lead five minutes before the interval but Aston Villa pulled parity through in-form Bertrand Traore on the 58th minute mark.
Manchester United swiftly restored their lead from the penalty spot thanks to Bruno Fernandes after Paul Pogba was impeded.
The Red Devils have not been defeated in the league since a 1-0 defeat to Arsenal on November 1; a run of ten games and are level on points with defending champions Liverpool.
"It's two extra points, if we'd lost and conceded a goal towards the end, Eric makes a fantastic block,” Solskjaer said after the game.
"I didn't enjoy the last 10 minutes that much because we should have seen the game out in a better way.
“It seemed like a cup final or the last game of the season, so we need to learn how to play out games better when we're in the lead.
"We've shown that when we're chasing a goal, we're capable of doing that. We created chances, I think it's always going to be a physical game.
“They've improved massively and they've given us some challenges and there were a few times in that box that you were a bit worried.
"We didn't stop the crosses well enough because when they put crosses into the box, they're always dangerous but we made some fantastic blocks, some saves and delighted with the three points obviously."
"Of course 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. We are getting fitter and fitter and stronger and stronger,” he added when asked about his men’s progress.
"These players have a great age. They are learning and are hungry to learn which is important. They come in every day with a hunger and desire to be the best on match day. They have been focused."
