Vincent Kompany drew encouragement from Burnley's performance despite a fourth successive home defeat that left them bottom of the Premier League table on goal difference.
Burnley find themselves still without a win in the league so far this season after going down 1-0 to Manchester United after a Bruno Fernandes volley.
They have taken just one point from their opening five matches - a draw at Nottingham Forest last week - but have shown encouraging signs at points without reward.
A more favourable run of fixtures are on their way, but the Clarets would have hoped to have started the Premier League season better given their dominant Championship performance last term.
Kompany insisted the performance against United underlined that his newly-promoted team are improving match-by-match and that results will come.
He said: 'We signed 14 new players in the summer and when I saw the fixture list - Manchester City, Aston Villa, Tottenham, Manchester United, Newcastle and Chelsea in the first 10 games, I thought it would be a difficult start.
'But when I look at the performance today I know results will come.
'We had good pressure throughout the game, we were never exposed and we were solid defensively. It was a good performance and I hope it gives the players confidence.'
Zeki Amdouni twice went close in the first half while substitutes Jacob Larsen and Jay Rodriguez had chances late in the game as Burnley pushed United all the way.
Kompany added: 'We had two or three massive chances and we could have had a result. We've shown signs of being an exciting team. The start is difficult in terms of results but I don't see any reason to think this team lacks character or margin to grow.
'We're prepared for this. We could win the first fiveRead on m.allfootballapp.com