Levein said: 'It's a very frustrating period for us. We are creating chances but not scoring goals. If we make any mistakes we seem to be getting punished.
"We hit the post twice and their keeper made a couple of brilliant saves, but we've got to keep believing that things will turn out alright for us.
"Of course we are now part of the relegation battle and it is important to keep cool, stick together and keep working hard.
"We're not getting what we deserve in matches and I'd be quite happy to play ugly and win 1-0."
Forest looked to have gifted City a 23rd minute lead when Andy Melville almost headed through his own net, but Paul Gerrard recovered in time to claw the ball away.
Gareth Williams then shaved a Forest post with a 16-yard drive and Alan Rogers rescued Forest when he cleared a Nikos Dabizas header off the line.
But five minutes before the break Forest took the lead against the run of play when a Rogers cross from the left found Gareth Taylor unmarked at the far post and the big striker had time to guide a powerful header beyond Ian Walker.
The second-half was all City, with Forest rarely breaking out of their own half.
But for all their possession City's best effort came just before the hour mark when Lilian Nalis struck a post and, with Williams unable to tuck away the rebound, Forest were able to scramble the ball away.