Following Chelsea's shock 1-0 defeat at Crystal Palace earlier on Saturday afternoon, City - who thumped Manchester United 3-0 at Old Trafford in midweek - would have gone ahead on goal difference with victory over the out-of-form Gunners.
However, despite taking an early lead through David Silva, it was Arsenal who showed the more desire as they recovered to turn in a strong second-half display and levelled through Mathieu Flamini.
Nevertheless City still hold matches in hand on their title rivals, and are just two points off the pace, although could be back further behind Liverpool should they beat Tottenham at Anfield on Sunday.
It is all shaping up to be a tense run-in, with the Reds also building momentum and would themselves be back in the driving seat if they can secure maximum points from key home games against City and Chelsea still to come.
Pellegrini said: "Four points from Manchester United and Arsenal when both games were away is a good week for us.
"Of course we could be more happy if we won today - and we had, especially in the first half, the chances to do it.
"Arsenal had a better second half, but no chances to score apart from the goal."
The Chilean coach added: "It is not easy to come to Arsenal's home and beat Arsenal.
"All of us want to win all the points, but, I repeat, we had a good performance against a very difficult team at their own stadium."
Pellegrini is expecting more drama before the final whistle of the campaign in May.
"The four teams have chances in the future to win the title, and four teams will drop points between now and the end of the season," he said.
"It is always difficult at the end of the season because there are a lot of teams in relegation positions who fight for every point.
"Ask Chelsea today what can happen away. We must just continue thinking about the next game.
"It is very difficult for me to know what will happen in the future. What I know is that if we win our matches it will just depend on what we can do."
Arsenal - thrashed 6-0 at Chelsea to ruin manager Arsene Wenger's 1,000th match last weekend - needed a response to make sure they were not overrun once again in a showdown with a top-four rival.
Indeed, but for a fine reaction save from England keeper Joe Hart to deflect a fierce angled drive from Lukas Podolski behind in the 60th minute, the Gunners could have gone on to win the match.
Wenger was pleased that his side finally showed the required character.
"We were a bit nervy at the start, insecure in our attitude by our last two results, but when even we when we were 1-0 down you could see the team was ready for a fight," said the Arsenal manager, whose side had conceded a last-minute own goal to draw 2-2 at home against Swansea on Tuesday night.
"We controlled the second half, we controlled the first 20 minutes and overall in the first half maybe they had another chance, in the second half we had a second chance.
"We could have won it in the second half, but overall it was a game of quality between two good teams and the game was played with a great spirit on both sides."
Arsenal remain in fourth place, five points behind Chelsea.
Wenger said: "Chelsea lost today at Crystal Palace, so that means all of us have to be careful and consistent.
"It just shows that we have absolutely to fight until the end of the season because everybody can beat everybody.
"Mathematically we are still in there, but it is not in our hands.
"We have to look above us and behind us as well, because behind us they are coming as well."