Jet2 later said that the unopened can was left there by a member of cabin crew who was handed it by a passenger.
The 59-year-old added that although the can appeared unopened he is shocked that alcohol is allowed in the cockpit at all and questioned why it had a napkin under it.
Steve, from Brackley, Northamptonshire, said: "We were waiting on board for 20 minutes to get off, that's when I noticed the can.
Steve Lewis said he saw the lager can by the pilot in the cockpit
"The plane had landed and the seatbelt light came on. I stood up to get my suitcase and as I did the cockpit door opened and I noticed the can in the cockpit.
"I turned to my partner Steven, who didn't believe me at first, but then he noticed you could clearly see the Stella branding.
"I was so shocked, I couldn't understand why there was alcohol in the cockpit."
Steve and his husband Steven, 51, had returned from their 11-night-stay in Benidorm for Pride.
He snapped a photo of the drink and sent it to Jet2.
Jet2 later said that the unopened can was left there by a member of cabin crew after they were handed it by a passenger
But Steve claims he was at first told it was not one of Jet2's flights - despite the iconic branding being clearly visible in the top left corner.
"An assistant got in contact with me and told me that the picture was not taken on a Jet2 flight. I felt like I was being accused of lying", said the doctor's reception manager.
"This is what upset me the most, I explained to her that I could prove it was taken on the Alicante to Birmingham flight.
"It even had a napkin underneath it which is how they serve drinks to passengers, so I'm a bit skeptical to whether it was there because someone had left it.
"It concerns me that alcohol is even allowed in the cockpit, if it was open or not.
"They flew 300 people home that flight and I just think there should be some rules on alcohol in the cockpit if there isn't some already."
Steve added that Jet2 eventually told him the can was there for "safe keeping".
Steve claims when he first shared the photo he was at first told it was not one of Jet2's flights
"[Jet2] explained that a senior member of staff had put the unopened can in the cockpit while passengers disembarked from the plane", he said.
"I just don't think it is appropriate to have any alcohol near the flight deck.
"I would like Jet2 to look into this and admit it was wrong [to have the can in the cockpit], they have said they are investigating but I haven't heard anything from them since."
A spokesperson for Jet2 said: "Upon further investigation of the photograph, we can confirm that it is an unopened can which had been handed to a member of our cabin crew by a customer when they were leaving the aircraft.
"This unopened can was then put down in the cockpit by the member of cabin crew, so that she could continue helping customers as they disembarked."