Paul Lambert claims he will not get complacent and warned his Norwich players 'there's an awful lot of hard work to do' for survival.
The Canaries chief watched his side cement their place in the Premier League's top ten and edge within 12 of the 40-point barrier, which usually guarantees safety in the top-flight, courtesy of a 2-1 win at West Brom on Saturday.
Andrew Surman volleyed home the opener to put Norwich ahead, before Shane Long drew Albion level from the penalty spot after Daniel Ayala's foul inside his own area.
However, Steve Morison scored his ninth of the campaign to seal the win for City, but Lambert is not getting carried away by their good form.
He told the Pink 'un: "We've won a few now away from home which is pleasing, but it is a really unforgiving league with some top, top sides in it.
"I'm pretty sure that people thought we were going to be in the bottom three at this time because we came up from League One really quickly so to sit where we are is terrific.
"I just try to concentrate on us and wherever we finish, we will see. I don't put pressure on myself or on my team.
"I've never been complacent as a person and hopefully the lads never think that, because there's an awful lot of hard work to do.
"They keep on going and they are a credit to the football club.
"It'll be only success if we stay in the league and we have given ourselves a chance to try and do it but there is an awful long way to go."