Forget recent history and national narratives, Sam Allardyce's relegation-free CV and Newcastle's new superstar manager; Norwich City are out to prove they can beat the lot – and you would be stupid to write them off, according to Patrick Bamford.

The Canaries' heartening result against Champions League-chasing Manchester City on Saturday was arguably the club's first positive full-time feeling since the home win over Southampton on January 2.

In what appears a three-horse race for one remaining Premier League survival spot, Sam Allardyce's Sunderland – who remain outside the bottom three on goal difference – had a free weekend while Rafael Benitez begins his Newcastle reign at leaders Leicester tonight.

'If people write us off then there is no pressure on us, and sometimes that can help,' said Bamford, following his first City start since joining on loan from Chelsea in January.

'As long as everyone in and around the city and the club believes in us and has that self-belief, then I think we will be fine. It doesn't matter what people in Newcastle or Sunderland say. They're a million miles away.

'You can see by the effort everyone is putting in that no one has given up yet. It's so tight down at the bottom. There are a lot of games and points to play for. So it's definitely not over and anyone who thinks that is a fool.'

It had been the call for a few weeks so come Saturday, it was time – and Bamford did not disappoint.

The 22-year-old on-loan Chelsea forward can finally say he has started a Premier League game, despite spending the first half of the season at Crystal Palace.

Bamford actually started one game for the Eagles – their Capital One Cup tie at, you've guessed it, Manchester City. On that day Alan Pardew's men were thumped 5-1 at the Etihad, so Bamford will have fonder memories of his second start against Manuel Pellegrini's men.

'We'll see how good that point is at the end of the season but I think we all needed this after the good performances in the last few games, and then that little slip of concentration at the end that has cost us,' said Bamford.

'We needed this point as a turnaround. Now we'll move on to next week with positive thoughts and build up a little bit of momentum.'

Things could have been even better for Bamford, had his stunning drive nestled under the crossbar, rather than striking the woodwork.

'When I hit it I thought it was going in and then it kept rising and rising... I was like, oh my God. Not today,' he smiled.

'That first Premier League start has been a long time coming for me really. I'm just happy. I'm thankful to the manager for giving me the chance. Now it's up to me to start rewarding him and paying him back through goals.'

He added: 'We had a game plan that was to sit off if we couldn't press but to try to give players like David Silva and Sergio Aguero as little time as possible. We could afford to give the centre-backs a little bit more time because back there, they can't really hurt us too much. But as soon as you let David Silva have the ball and turn, it becomes a different game.

'So I think you saw the energy we put into it in the first half to try to stop that and it worked.'