The Red Devils are now ninth in the table, 12 points behind the Gunners, with all teams in the division having played 14 games.
It does not look promising for United's hopes of defending their crown, but Pellegrini thinks the title battle remains "exactly the same".
Asked on Friday about Wednesday's results and if he thought United were now out of the race, Pellegrini - whose side triumphed 3-2 at West Brom - said: "It was an important game for us, winning the three points away.
"I think the fight for the Premier League is exactly the same. There are eight or nine teams that are very close in points.
"For us, it is very important to continue winning.
"But we have five more games to complete the first half (of the season) and then we have all the second half."
Pellegrini was speaking at a press conference to preview Saturday's top-flight visit to Southampton.
Prior to the West Brom result, City - who are third, six points behind Arsenal - had won only one of six Premier League away games in 2013-14, losing four of them.
Beating Albion was certainly a boost ahead of the Saints trip, although Pellegrini has stressed that even prior to the match at The Hawthorns, there had been no issues with his players' confidence regarding their ability to secure victories on the road.
"I think that before the West Brom game, we didn't have any problems psychologically about winning away," the Chilean said.
"Maybe you think there is a different reason, but I was absolutely sure it was just about the points - not tactical problems, and I am also sure the squad had the confidence.
"We were sure we were going to start winning. So then that (West Brom) was first, and now we must repeat it tomorrow."
Eighth-placed Southampton go into the encounter off the back of three straight defeats - a notable run of results in the tenure of Mauricio Pochettino as their manager.
The 41-year-old Argentinian, who previously coached in Spain at the same time as Pellegrini, has done an impressive job overall since succeeding Nigel Adkins in January.
Southampton beat City 3-1 at St Mary's shortly after that appointment and Wednesday's 3-2 reverse against Aston Villa was the Saints' first home defeat this term.
Pellegrini does not know how Pochettino's men will react on Saturday, but sees it as a dangerous thing that they are hurting from a succession of losses.
The 60-year-old said of his fellow south American: "I know him very well. He is a very good manager and I think he is doing a great job with Southampton - he also did in Spain.
"I am sure we are playing against a strong team.
"I think playing against a team as good as Southampton, when they have lost the last three games, will be more difficult for us.
"I don't know what the reaction of Southampton will be. They are a young team, and they have a young manager.
"But he knows perfectly how he must manage this situation."
Pellegrini is optimistic City captain Vincent Kompany will be fine to keep his place in the team for Saturday's match.
The Belgium defender, who has been sidelined by a thigh problem, made his first appearance since October 5 on Wednesday when he played for the whole of the West Brom contest.
Regarding Kompany, Pellegrini said: "We will see if he can play two matches in less than three days. But he is okay.
"It is not an easy decision. But I think he finished the last game without any problem.
"We will wait to see that he has made the perfect recovery and I will decide. But I don't think it is a great risk for him to play another game."
Striker Stevan Jovetic, defender Matija Nastasic and playmaker David Silva will all miss out due to their calf injuries, but Pellegrini has indicated the latter of the trio could be involved in Tuesday's Champions League match at Bayern Munich.
The manager once again would not confirm whether Costel Pantilimon would be retained in goal or Joe Hart brought back in his place.