'Los Colchoneros' could only muster a 1-1 draw with Premier League champions Chelsea at Stamford Bridge which, combined with Roma's 1-0 victory over Qarabag, condemned them to a third-place finish in the group, meaning that they drop into the Europa League.
Griezmann spent the summer being heavily linked with a move to Manchester United, but committed his future to the Madrid-based side after Atletico's transfer ban was upheld.
Since then though, the Spanish side have agreed a deal for Chelsea striker Diego Costa, leading to speculation that Griezmann may now be allowed to move on, with Barcelona and United once again being linked with his services.
However, speaking following Atletico's Champions League exit, Simeone denied suggestions that it could encourage Griezmann to pursue a move elsewhere.
'On the contrary. It is a new challenge,' he told the press.
'Everything that is bad, we make it into a positive.'
The French international has scored just seven goals in 18 games in all competitions so far this season, a disappointing tally by his high standards, though his form has shown signs of improvement of late, with the 26-year-old scoring three times in his last two league games.