City missed the chance to take over at the top of the table following Chelsea's shock defeat at Crystal Palace earlier in the day as they had to settle for a draw against the Gunners.
David Silva gave City the lead in a first half they dominated, but Arsenal responded well after the break and claimed a deserved share of the spoils through Mathieu Flamini.
Pellegrini's men are two points behind the Blues in third with two games in hand, but second-placed Liverpool will take over at the summit if they avoid defeat against Tottenham on Sunday.
The Chilean coach told Sky Sports: "I always said that this would be a very close Premier League with three or four teams fighting until the end for the title.
"I think Arsenal still have a chance to fight for the title. We will see which team does things better from now until the end.
"The most important thing is that we continue depending on what we can do between now and the end of the season."
Pellegrini was happy enough with the draw against Arsenal, particularly as it came after a resounding derby success against Manchester United at Old Trafford, but felt his side did enough in the first period to have won the game.
He added: "I think it is a good point. We played two games away this week against Manchester United and Arsenal. I think four points from six against two big teams is not bad.
"I think with a bit more luck today we could win the game because before they scored we had a clear chance to make it 2-0.
"It was a very close game. I think we played better the first half, but the second was very equal.
"We had four or five clear crosses from the right side in the first 25 minutes that we didn't finish well, but football is like that.
"If there was a team which deserved to win, it was our team."