Arsene Wenger's men remain four points clear at the top of the table after winning 3-0 at Cardiff City on Saturday.
With fellow title hopefuls Manchester City and Manchester United having previously dropped points against Malky Mackay's side this term, Szczesny believes his club passed a stern test of their title credentials.
"We spoke about it before the game - we knew that Man United and Man City dropped points at Cardiff and that it would send a very strong message to our rivals if we won," he said.
"We're in a position that we'd like to be in for as long as possible. But it really doesn't matter where we are now. It matters where we are in May.
"If we carry on like we are now then I'm certain we'll be top in May. But we have a lot of work to do, a lot of tough games to win. There's no point in putting pressure on ourselves.
"We just want to enjoy every single game; that's bringing the best out of us and I don't think that will change."
The Poland international insists Arsenal will not make the mistake of looking too far ahead.
He added: "We want to focus on the next game, which is Hull (on Wednesday), and to keep on winning. If we do that, get the right result then we'll put ourselves in a very comfortable position at the top of the table.
"It's very good to have that cushion at the top of the table. If we want to win the league then we must do our job very professionally to beat teams like Hull.
"If we get the three points then we'll be in a very comfortable position for you guys (the media) to talk about the title challenge. We just want to focus on the next game."
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
