The midfielder scored a blistering second goal after David Silva had flicked in Toure's shot for the first, with Vincent Kompany's header sealing a comfortable 3-0 win for City.
New £49million forward Raheem Sterling was overshadowed by City's old guard with Silva and Toure at the heart of City's best efforts.
Silva deflected in Toure's shot - which also got a touch off a defender - for the opening goal with the visitors' dressing room giving the Spain star the credit.
And Pellegrini reckons, after a stuttering season last year, Ivory Coast star Toure will shine in the Barclays Premier League again.
He said: "I always said last season it was a strange season for Yaya, he started with a lot of problems, the death of his brother, his agents
I think he was not focused on what he had to do last year.
"We spoke before the start of the season and I am very sure we will see the Yaya from two years ago
He is a very important player for us.
"I don't think Yaya deserved the amount of criticism he received last season
It was not his best season but he did not play so, so bad like everyone said.
"He is an important player for us
It is very difficult for a player when you have so many problems."
Sterling, replaced by Samir Nasri in the 74th minute, should have marked his debut with a goal but was thwarted by Boaz Myhill when put clean through by Fernandinho.
Pellegrini insisted he was happy with the 20-year-old's contribution.
He said: "I'm not disappointed because Raheem played 74 minutes very well
It is not easy for him to play a new style with new teammates, he worked a lot and he had two clear chances.
"If he continues to play like this I am sure he will be the player we bought."
Saido Berahino saw a goal ruled out for offside and shot straight at Joe Hart while Albion debutant Rickie Lambert went close with a free kick.
But the Baggies were second best and boss Tony Pulis, who also gave James Chester and James McClean their debuts, admitted he got it wrong.
"I take responsibility for the way we set up
The fact we had Saido and Rickie up front together pulled us away from what we should do," he told Sky Sports
"I said to them afterwards I'd take responsibility.
"There are certain principles we have to stick by and work with to get results at this level and I went away from that
We created quite a few chances but we were far too loose as a team."
Albion completed a club record £12million deal for Zenit St Petersburg striker Salomon Rondon hours before the game and Pulis expected more changes to his squad.
He added: "We know what we need to do in the transfer market
The chairman has been very good
We're after quite a few targets and there will be players who leave the club as well."
Source : PA
Source: PA