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Bowyer, who is about to embark on his sixth season at Elland Road, said: "We have to push on to win the league now. I think we are a good enough side and it's time now we proved it.
"Last season we let ourselves down against the smaller sides but did well against the top clubs, but this season I think we will be pushing a lot harder."
Bowyer insists that the current Leeds squad, boosted by last November's £18million arrival of Rio Ferdinand, is good enough to win the Premiership crown.
"Rio's been a great buy," Bowyer added on the club's official website. "He's a brilliant lad and it was money well spent bringing him to the club.
"It wasn't an easy season but everyone played well. I think that we coped very well and that stands us in good stead for the next campaign
"There's a great belief here. All the lads that came in have fitted in well and we have a brilliant spirit."