City's loss at Villa Park, sealed by Matty Cash's first-half strike, marked their third consecutive defeat away to Villa and left the former champions under pressure early in the campaign. Arsenal, meanwhile, edged past Crystal Palace by the same scoreline to extend their advantage at the top.
Guardiola, however, has reminded supporters that the season remains long and unpredictable.
"Arsenal have been solid for many years," he said. "The concern is how we can improve, better, better, better, and stay close. From my experience, the season is so long. There are many teams competing."
The Spaniard also admitted that his real concern came earlier in the campaign. "I was worried before the international break in September when we were 14th in the table," he added. "If Arsenal win all their games and win the Premier League, we congratulate them. But I feel the team is alive and playing with courage and possession. We just need to be more stable."
City struggled to break down a well-organised Villa side, with Erling Haaland denied for only the second time this season after a remarkable 12-game scoring streak for club and country. The Norwegian forward even saw a late equaliser ruled out for offside after colliding painfully with the post.
"I didn't speak with him," Guardiola said. "He got a knock from the post. We've scored a lot of goals this season, and Erling, of course, is important, but today was difficult because Villa defended very well."
For Villa, the result was a perfect way to celebrate Unai Emery's third anniversary in charge. Since taking over in October 2022, the Spaniard has transformed the club from mid-table strugglers into genuine top-four contenders.
"We started the season poorly and had doubts," Emery admitted. "But this week, against Tottenham and Manchester City, the players showed fantastic commitment and followed the gameplan perfectly. That gives us confidence and positive energy. Villa Park is becoming our fortress again, and we must keep raising our level."
City now turn their focus to next weekend's home clash against Bournemouth, while Arsenal face a trip to Burnley as the title race begins to take shape.
Enzo Maresca has made it his mission to help Phil Foden rediscover his best form and re-establish himself as one of England's leading players after the Manchester City midfielder ended his goal drought in spectacular fashion.
Vincent Kompany has played down fears of serious injuries to Luis Diaz and Min-jae Kim after Bayern Munich's 2-2 draw with Arsenal in the Champions League on Wednesday.
Virgil van Dijk believes Rio Ngumoha has a bright future at Liverpool after the teenage winger played a key role in their thrilling 4-3 Champions League victory over Villarreal at Anfield.
Chelsea face Tottenham this weekend with several injury concerns to manage, although Malo Gusto is expected to return as Xabi Alonso attempts to improve his side's inconsistent form.
