Villarreal players felt Bayern underestimated them in their Champions League quarterfinal tie, and Emery has warned that Liverpool will not make the same mistake.
"We deserve to be here," Emery said. "Any side that is in a Champions League semifinal is there because they deserve to be.
"Liverpool know we have a great European presence, that we have been able to eliminate two great teams [in Juventus and Bayern.] They know it won't be easy. This is the best Liverpool side that I can remember. They will feel like favourites, of course, but will have respect for us."
Villarreal made headlines last season by beating Manchester United on penalties to win the Europa League, their first European title.
"It's not by chance that we are here," Villarreal midfielder Dani Parejo said. "We made club history last season by winning the Europa League and now we have reached the semifinals of the Champions League for the second time in Villarreal's history. It's all down to stability, hard work, trusting a project and giving people time to work."
"We face a bigger challenge than before," Emery added. "The surprise factor is no longer there. They are the number one favourites to win this competition. The team is a mirror of their coach, Jurgen Klopp, in terms of playing with joy, with enthusiasm. They are in the best moment."
Emery, who spent 18 months in charge of Arsenal until he left in 2019, does not have fond memories of his visits to Anfield.
"I remember my experiences against Liverpool at Anfield as challenging," he said. "I recognise the work done and the identity created by Klopp, which has since been further improved.
"I see that as an additional motivation for me, to try and beat the best-ever Liverpool. For that we will need to show our best version."
Villarreal have not won any of their last eight away games in England in all competitions but will take strength from their solid performances in their 3-0 win at Juventus and their 1-1 draw at Bayern in their last two away European outings.
"Anfield is special and the atmosphere is impressive, incredible," Villarreal midfielder Dani Parejo said. "It's difficult not to be affected by the atmosphere there but we will try to put the focus on the game and on our game plan."
Villarreal travel to Liverpool not at full strength with winger Yeremy Pino out injured and striker Gerard Moreno not fully recovered from a hamstring problem.