The 37-year-old crashed in Sunday's marathon to make it a disappointing return from his three events, as he was unable to build on his four golds from London in 2012.
Weir will not take part in the next Games in Tokyo, either, having recently announced his intention to retire from the sport after next year's London marathon - also ruling him out of the World Championships at the newly-named London Stadium.
Speaking to BBC Sport after his latest disappointment, the Englishman said: "It's an individual sport, and I realise that now. I always praise every athlete to put on a British vest but sometimes I feel like I've been stabbed in the back. We need to click as a team.
"I know it's an individual event but there needs to be no big egos within the team. We need to all work together - like the US team, the Aussie team. I don't care if you're from Scotland, [Northern] Ireland or anywhere else - I just want to see Britain win a lot of medals in wheelchair racing.
"I'm never jealous of anyone and if somebody beats me I'm happy - as long as they are competing for a medal. I want the team to do well and I want wheelchair racing to be successful all around the country."
Britain's wheelchair racers won eight medals overall in Rio, including three golds for Hannah Cockroft.