The Gunners beat Everton 3-1 on Sunday but still finished fifth after Liverpool cruised past Middlesbrough and Manchester City hammered Watford.
It is the first time since 1996 that Arsenal have failed to finish in the top four and it remains to be seen how the prospect of Europa League football will affect the squad this summer.
Arsene Wenger is yet to confirm whether he will still be manager next season while the futures of Alexis Sanchez and Mesut Ozil are also uncertain, with both players stalling over new deals.
Cech believes Arsenal can follow Chelsea's lead and bounce straight back into the Champions League - but only if the squad is kept together.
"If you have one odd year in 20 years, it is not a problem," Cech said.
"I think the club has a strong foundation, a strong organisation and everything to be one year out and come straight back in, like Chelsea did last season.
"Obviously, it helped them not to be involved this season because they could keep all their energy for the league.
"For next season, you need to respect every competition as we've always been doing and carry on the momentum, trying to win as many games as you can and keep the team together.
"That's the main thing - we need to keep the team together and try to strengthen it in the areas where the manager would like to and then we will be ready to go again."
On Sanchez and Ozil, Cech added: "Obviously they are both fantastic players this season.
"Alexis has been brilliant, scoring a lot of goals
They are both exceptional players and obviously you always want to keep your exceptional players."
Arsenal won seven out of their last eight Premier League games but paid the price for a miserable run through February and March.
They finished with 75 points, four better than last year when they came second, but managed only two wins from 10 against the top six.
"We have four more points than last season so in a way you would think that we improve by four points and we would be in a similar position like we were last season," Cech said.
"But unfortunately the other teams ahead of us had a very good season
They managed to get points and we had a few results which didn't go our way
It was our mistake.
"When you lose games where you make too many mistakes and drop points unnecessarily, that was a mistake, particularly the games at the end of February and March when we slipped behind and we had to chase.
"In the big games last season, we managed to have the most points out of the top six but in the head-to-head games we didn't do so well and that probably makes the difference because we gave points to our rivals and they took advantage of it."
Source : PA