Allen received a warm response from his home crowd as he returned to the venue where he became back-to-back champion in 2021 and 2022.
It was clear the respect that both players had for each other following the match with Allen adding he "wished Jordan well, I always do".
The world number 65 said the win was "the least satisfying" he has ever had as he progressed to the last 32 to face Michael Holt.
"It is overwhelming for Mark here with his family, friends and all the fans who have paid good money to see him play," said Brown.
"It is very difficult. I have my own battles to go through. I am in a precarious place in the rankings, and I lost my mum recently. It just puts everything into perspective.
"The general public seem to think we are just robots who just turn up to pot a few balls, it is not like that at all."
Matches between Brown and Allen have always been close contests, with Tuesday's win the 39-year-old's first victory over his close friend.
"I really hope so," Brown replied when asked if he thought Allen would reconsider retiring.
"The first words I said to him today was it was great to see him back and we had a big cuddle. It is tough to see him going through that.
"I have no doubt he will come back. Snooker is his love, he is absolutely brilliant and he is a top bloke, I wish him all the best."