The Reds looked well on course to secure a top-four finish at Old Trafford when Weir scored twice after coming off the bench to replace injured striker James Wilson. However, the Canaries netted twice in the final 10 minutes to force a rather undeserved draw despite losing Raymond Grant to a red card.
Warren Joyce's side must pick themselves up for a dramatic final fixture at Reading's Madejski Stadium next Thursday, knowing victory will keep hopes of retaining the trophy alive.
"It's really tough to take," Weir conceded to MUTV. "We were 2-0 up with 15 minutes left – we should see out the game. We got unlucky with the penalty and then another deflected goal. We just need to keep our heads up and go on and beat Reading now.
"They sat back quite a lot for the whole game. When Willo went off, I didn't think we'd be able to get a goal after that. Luckily, I got a tap-in and then another goal and we opened up the game a bit. Maybe we opened up a little too much as it's finished 2-2.
"One of them was probably the easiest goal in football. I think Louis Rowley's got the flick-on and I wasn't sure if it was going in anyway so I made sure I got it across the line. The other one, I think it was Guillermo Varela who did really well on the right side and cut it back. I got in there