Striker Delighted To Get Off The Mark For Season"Their game went to extra-time so hopefully they will be more tired than us," said Barnett.
"It’s a very good place to play and our result at Blackburn will give us a boost to go there and hopefully do the same again.
"The league is our bread and butter - it was disappointing to lose on Saturday, but hopefully we can put that behind us and get the right result at Bradford."
And Barnett hopes the Bantams will have a little less energy after they went all they way to penalties before going out of the League Cup to York City.
Town return to Sky Bet League 1 duty on Saturday with a trip to Bradford City.
"A cup run is always good for the team, the spirit, the club and the fans so hopefully we draw a big club in the next round," he said.
“Blackburn is a hard place to get the right result - we knew we’d be hard pressed to beat them so it’s all credit to us."
And Barnett is hoping for a big draw for the Club in the second round.
Town enjoyed a good run in the Capital One Cup last season as they reached Round 4 - beating higher-division sides in Blackpool, Leicester City and Norwich City along the way.
“They kept going right to the end and we did well to keep them out," admitted Barnett.
“We could have had a couple more goals but so could they.
“They brought on some good players but luckily for us we were able to weather it.
“Jayson (Leutwiler) pulled off some good saves - he was inspired on the night for us."
Blackburn looked to force the game into extra-time approaching the end but Shrewsbury were able to hold on.
“I was very happy to get off the mark and with another striker scoring as well, it was a good night for the forwards," said Barnett.
“I’ve been practising them like that with my left foot in training so it was good to see one of them come off."
And Barnett, who rifled in a left-foot shot for the winner, admitted he had been practising the technique in training.
The 29-year-old got Town's second goal of the night at Ewood Park on Tuesday evening after James Collins' early opener had been cancelled out by Nathan Delfouneso.
Striker Tyrone Barnett was delighted to get off the mark for the season as his winning goal at Blackburn Rovers fired Shrewsbury Town into Round 2 of the Capital One Cup.