Venkatesham this week said the Gunners would lose out on "tens of millions of pounds" should they not finish in the top four and, while it would not impact the club "catastrophically" if they did not return to the top table of European football this season, sustained failure would hamper their business model.
Asked if that makes his job harder, Emery, who takes fifth-placed Arsenal to Bournemouth on Sunday, told a news conference: "I learned in my past that I am not [under] pressure.
"I learned that I need, for me and for every player and people that work close with me, to have very big demands.
"Here, I want to transmit to every player, the high level we need to work, the high level we need to stay [at]. It isn't pressure, it is our demands, our big demands every day."
Emery shares Venkatesham's desire to finish in the top four, though.
"We want to [but] it's not easy," he said.
"We are going to work and we are going to find, in each training, each match, to be close to the top four."
Arsenal head into the weekend one place and four points above their opponents and Emery is not surprised by how well Eddie Howe's team have performed.
He said: "They are a very organised team, they work hard, they work tactically in every game.
"For us, Sunday is a very big test, a very high-level test for how we can continue in our process and our progress.
"It's very important to show every supporter our mentality on Sunday.
"I think they are a good team, a young coach but a very good coach.
"I know Bournemouth and they are a very prepared team with tactically good movement on the pitch and with a big intensity.
"We need to prepare well, we need every player with a big mentality to fight strongly there against them, with our quality but above all, with a big intensity and a big mentality in the 90 minutes."
Left-back Nacho Monreal will miss the game on the south coast while Stephan Lichtsteiner is doubtful. Both men have hamstring injuries.