Back-to-back home wins over West Ham and Middlesbrough last week saw Marco Silva’s side move out of the bottom three in the Premier League table for the first time since October.
And despite falling to a 3-1 defeat to Manchester City last weekend, the Tigers remained out of the drop zone as 18th-placed Swansea City lost 1-0 at West Ham.
With six games to play, the Tigers have their destiny firmly in their own hands but Maguire insists plenty more hard work is needed if he and his team-mates are to achieve their goal.
“We’ve given ourselves a great chance of staying in the Premier League,” he said.
“We put ourselves in a great position with the West Ham and Middlesbrough wins, which saw us move out of the bottom three and we know we have to build on that.
“There is a real sense of belief here, and credit must be given to Marco Silva and his coaching staff for installing that belief in us.
“Nothing has been achieved yet though. We know that we need to continue to work hard to get the results needed to secure Premier League football next season.”
Maguire also had words of praise for the black and amber faithful for the support they have given the side this season, and believes they have a vital role to play as the Tigers look to achieve their goal in the run-in.
“The fans have been huge for us this season,” he added. “Our home form has been good this season, and some credit for that has to be given to the fans.
“They’ve been our twelfth man at the KCOM Stadium at times, and whenever we’ve needed a rallying call, they’ve been there for us and provided it.
“We’ve all got to be together in the next six games as we look to achieve our goal. The fans have got a huge part to play though.
“We’re always grateful for the backing they give us and hopefully we can reward them for their support by staying in the Premier League.”