The Pep Guardiola era began with a win on Saturday as Manchester City eked out a 2-1 victory over Sunderland on the opening day of the Premier League season.
An own goal three minutes from time from Paddy McNair - who signed for Sunderland from Manchester United earlier in the week - gave City victory after Jermain Defoe had cancelled out Sergio Aguero's opener.
"We definitely deserved the victory," Guardiola told BT Sport.
"The first games are always difficult. Sometimes, you are little lucky. We should have been a bit more aggressive but these kinds of things have to happen to know how to get better in the next game.
"We are a team. We fight like a team and they did it. For the new manager, new players, it's important to believe in what we are doing."
Leicester City began the defence of their title with a 2-1 defeat at newly-promoted Hull while Swansea and West Brom also claimed opening-day wins.
Guardiola dropped goalkeeper Joe Hart for his first match and Aguero gave him the perfect start after four minutes when he converted a penalty, awarded when Raheem Sterling was fouled by Patrick van Aanholt.
Defoe then equalised with 20 minutes to go - scoring for the 16th successive season - but Jesus Navas's cross rebounded off the head of McNair to give City the win.
Leicester manager Claudio Ranieri had warned that repeating their surprise success of last season would be nigh impossible and Hull showed just how hard it will be as they came away with a 2-1 win.
Adama Diomande put the Tigers in front at the end of the first half when a shot by Abel Hernandez flicked off his foot and over Kasper Schmeichel in the Leicester goal.
Two minutes after the restart, Riyad Mahrez equalized from the penalty spot after a foul by Tom Huddlestone, but Robert Snodgasss won it for Hull with a fine strike from the edge of the box.
"They played better," Leicester manager Claudio Ranieri told the BBC.
"We made two mistakes and they scored two goals. We missed two early chances to score.
"I told my players this season will be harder than last season. Today was a normal match, maybe a draw (would have been) normal but we lost it."
Dutch Midfielder Leroy Fer gave Swansea a 1-0 win at another newly-promoted side, Burnley.
Swansea manager Francesco Guidolin described it as "an important victory".
"We're more confident for the future," he said.
"I'm happy for Leroy, I feel he could get many goals because he is strong in the air and he often gets into the penalty area."
Salamon Rondon's 74th-minute goal secured a 1-0 win for West Brom at Crystal Palace.
Eric Lamela scored the equaliser as Tottenham came from behind to draw 1-1 at Everton, for whom Ross Barkley had scored the opener after five minutes.
Southampton drew 1-1 with Watford and the other newly-promoted side, Middlesbrough, began with a 1-1 draw against Stoke.
Arsenal meet Liverpool on Sunday while Jose Mourinho kicks off his Manchester United reign with a visit to Bournemouth and Chelsea play West Ham on Monday.