Emery said: "I am satisfied and proud. Satisfied with the job that we have done and proud of the project that we have here at Villarreal.
"The president had been here for over 20 years, they have been in the Champions League semi-finals, three Europa League semi-finals but lacking that final step.
"I think we are going to be up against the favourites in Manchester United and they have shown their potential throughout the campaign in this competition.
"However, we have knocked out one of the teams that was one of the favourites, we are aware of how difficult it is going to be but we are proud to prepare and compete in that kind of game.
"Manchester United are a great side and we are going to have to work hard to nullify some of their strengths."