The Cumbrians pushed City all the way in their pre-season friendly at Brunton Park, taking a 1-0 lead through Matty Robson before Hull managed to grab two second-half goals to turn things around.
But Abbott was left to enthuse about his side's display and feels that if he can add a striker to his squad then they should be well placed to succeed.
"We're looking for a striker, everyone knows that," he told BBC Radio Cumbria. "We know we've got to put the ball in the back of the net and that was the bit that was missing.
"But if we keep playing like that, we'll be a really good side this season. I feel very optimistic, we probably played some of the best football since I came to the club.
"We could have won the game quite comfortable against a Premier League side who have got some quality players and at times we made them look quite ordinary."