The Tigers dropped back into the second tier on Sunday with a heavy 4-0 defeat away to fellow strugglers Crystal Palace, 12 months after earning promotion.
Despite Silva's impressive work since being recruited in January, taking 21 points from the 51 on offer, the Portuguese - soon to be out of contract at the KCOM Stadium - was unable to keep the Humberside outfit in the division.
Allam did not provide any update on the ongoing talks with Silva, but he did vow to keep supporters in the loop as they prepare for another season of Championship football.
"Yesterday's result was hugely disappointing having fought so well in recent months for Premier League survival," a club statement read. "Myself and everyone at the club feels the pain of relegation and we also know how much supporters are affected too.
"We have one more game remaining in our Premier League campaign and every effort will be made to ensure we end it at the KCOM Stadium on a positive note. Despite my disappointment at suffering relegation, I cannot praise Marco Silva and his staff enough for the job they have done since arriving at the club in January.
"At that time, with the club sitting at the foot of the table, many had completely written off our survival chances, but Marco came in and gave everyone hope with improved results and performances. Although we have ultimately fallen short in our goal to remain in the Premier League, the improvement seen in the team under Marco's leadership has been clear for all to see.
"Going forward, I will provide more frequent communication to supporters over the summer as we all rebuild for the challenge ahead.
Hull welcome Tottenham Hotspur to the KCOM Stadium next Sunday in their final Premier League outing.