Watford dealt Hull a big psychological blow in the race for a top-two finish at the KC Stadium last week with a 1-0 win that lifted them to within a point of Steve Bruce's second-placed side.
But Brady struck the only goal of the game against Middlesbrough as the Tigers hit straight back - Watford dropped two points after being held 0-0 by Cardiff - and they head to Portman Road with a spring in their step.
"We're still in second place and we knew Saturday was a massive game," Brady told the club's official website.
"The win has given us a boost of confidence going into our next game against Ipswich and hopefully we can get another good result there.
"After that, there will only be four games left, so it's getting close now."
Brady added: "It was annoying to lose to Watford with them being so close behind us.
"It wasn't the best of feelings, but we knew we had to pick ourselves up quickly.
"There was no time to be moping around and three points on Saturday was vital."