"It was amazing, I'd like to thank the manager for believing in me," he told BBC Radio Shropshire.
"My confidence has gone through the roof. It was a dream start, I'm just lost for words."
Bradshaw started his career with Welsh Premier side Aberystwyth before joining Shrewsbury.
He is their first player this season to score more than one goal in a game.
"It has always been my dream to play professional football and there's no better club than Shrewsbury," he said.
"The win gives us a chance to get a play-off place and that's what we are aiming for."
Source: BBC Sport
Source: BBC Sport