Freddie Sears gave the visitors a 25th-minute lead against the run of play after the Blades were caught on the break following a corner.
Harry Maguire equalised in the last minute of the first half thanks to an error from keeper Sam Walker, who helped the ball into his own net from the defender's shot.
And Weir said: "I thought we should have nicked it. Towards the end we were the team pressing.
"For their goal, it was just a bit of naivety with regards to the situation and the decisions we made and we got punished for it.
"I thought we came into the game really positively after that and we did the right things. Fortunately we got the goal just before half-time
"We pushed on in the second half and there were many positives. Five under-21s started and another one came on.
"Those young ones, allied to the senior players, were really good.
"It's a compliment to Sheffield United as a club that people come here and make it difficult for you to win. It's obviously something that we've got to adjust to and get used to.
"I think we can always create more and I think that will come. We've got exciting players and they're learning."