An Ofsted inspector also found the quality of teaching to be weak at Music Box nursery in Salisbury Street, and that communication with parents was not always effective.
Staff did not regularly observe and assess children's learning or plan challenging activities, or keep a note of the youngsters' attendance which made it difficult in the event of an emergency.
Inspector Trish Turney visited the Music Box at the start of February and published her findings this week.
She said in her report: "Children do not receive the support they need to make progress in their learning, particularly in their communication and language development. They do not develop confidence or learn to participate in activities for long periods of time. They have little motivation to play and learn.
"Children do not gain the key skills to help prepare them for the next stage of their learning or eventual move to school."
She added: "Staff do not always implement effective measures to keep children safe. The premises are not always secure. Unauthorised persons can enter the building and the nursery rooms without staff's knowledge.
"Staff do not promote children's good health and well-being effectively. The temperature in the nursery is too low and staff do not ensure children have regular access to drinking water."
Ms Turney highlighted the one strength of the nursery as children being able to develop some physical skills by playing on wheeled toys or by rolling balls.
Music Box looks after a total of 15 children aged two to three, but has the capacity to take on 40.
While visiting, the inspector observed the quality of teaching, held a meeting with the provider and deputy manager, and spoke to parents.
In her report she added that, for the nursery to reach suitable standards, a system must be put in place to assess children's learning and make their time there a 'challenging and enjoyable experience', while also involving parents and ensuring any needs are addressed quickly.
Music Box did not respond to requests for comment.