Manuel Pellegrini has challenged his Manchester City players to begin an era of dominance after watching them wrap up a second Premier League title in three seasons.

After goals from Samir Nasri and Vincent Kompany defeated West Ham United 2-0, ensuring that City to ended the season on 86 points, two ahead of Liverpool, Pellegrini said: "Big teams cannot be satisfied with one title. It's very important. Celebrate today, tomorrow and Monday and on Tuesday start working for next season because this club and players deserve more titles."

Kompany echoed his Chilean manager. "It's a great achievement. It will be recognised," said the captain. "We're building a big club and I'm proud to be part of this. We did everything right this season."

Pellegrini, who in leading City to the championship won a first league title in a decade of managing in Europe, picked out two pivotal moments from an incident-packed campaign.

The first was following the 2-1 defeat to Chelsea on 27 October, which consigned City to four points from their first six away matches. The second was after last month's loss at Liverpool.

He said: "For me there were two key moments, one of them when we played the first six games away and had just four points. I spoke with the players and we continued playing the same way. I don't think we deserved to lose those points. From that moment, I think the team has the most points playing away.

"The second moment was after we played away against Liverpool. We didn't deserve to lose 3-2, we didn't have the option to win the title but we never gave up the hope Liverpool could lose points. It was not the best week but we won the last five games."

Pellegrini explained how he has transformed City from the team that finished 11 points behind Manchester United last term, under predecessor Roberto Mancini, to champions.

"It was not easy," he said. "The most important thing was we changed the way this team played. I like to play another way and it was very important to give the reasons and have the trust of the players. Maybe if we didn't win the title it would be a very good reason because it was my first season but I did not want to give an excuse. I think it was a season that all of us enjoy, the fans, the players, me also because they see the way we play.

"I manage a great group of players, a great institution and great fans. I must be calm during the game to take decisions but when you achieve the title…"

Pellegrini has become known for his cool demeanour, but he did admit losing his temper when City were knocked out of the FA Cup in March. "The worst moment was when we lost against Wigan here in the FA Cup," he said.

Pellegrini also stressed he likes the team to play a progressive style. "It is very important to go for the match from the beginning, it doesn't matter against whom you play. We have players to play in counter attack but for me, to win titles just in that way, I will not be happy. We won with 102 goals, with the record of [156] goals in all competitions in the history here in England. It is the way the team must play with the quality of players we have."

Kompany, who led the club to a first championship for 44 years two seasons ago, added: "Forget about the money and everything. As a kid, you grow up and dream of lifting trophies, I feel like I am living that dream when I do this."

The on-pitch celebrations included Pellegrini being given the bumps by some of his players. "It was a moment to celebrate. After we win, any kind of celebration is allowed. I will celebrate with my family. My whole family is here and from tomorrow [Monday evening] we will go to Abu Dhabi, the whole group, for two or three or four days," he said of a trip that includes a friendly match against Al Ain.

While Sam Allardyce's future as West Ham manager is under threat, he offered a defence of his team's campaign. "We've had no real threat of relegation for a while," he said. "We did the job after our difficulties in December and January. We've won seven out of the last 15, which is nearly a 50% win rate. So we've pulled ourselves out of the bottom three in the league and finished 13th. We've got 14 clean sheets. If we had converted some of those into 1-0 wins, we'd have 46 points again.

"I suppose the problem is having your best run at the end of the season rather than at the beginning."