The Magpies defender was sent off for a high challenge on Kevin McDonald 12 minutes into the League One opener.
Weir admitted that playing against 10 men can bring its own pressure, but said that his players responded well to the task.
"It had a big influence," Weir told Sky Sports News. "These things happen in games and that put a bit of pressure on us as well, in the respect of a lot of people thought the game was won.
"It was a tough game, with a lot of challenges and I thought we came through it well. They asked a few questions and I thought we answered the majority of them.
"During the course of the season we will have to adapt, we will have to change and we will have to do what's required in certain games. But I thought tonight we played well, we passed the ball really well, moved the really well and created opportunities."