Messi's future at Barcelona has been a subject of severe speculation off late and it has dominated headlines in the current season.
Conte feels Inter Milan stayed calm despite their opponents taking a lead and continued doing what they had trained for.
Juventus striker Cristiano Ronaldo broke through just before the break, to score in a seventh consecutive league game.
Barcelona are already through to the knockout rounds after six-time Ballon d'Or winner Messi scored in a convincing 3-1 victory over Borussia Dortmund last time out.
Inter Milan -- fourth last season -- suffered an early upset after Domenico Berardi slotted in a 27th-minute penalty to give all three points to their rivals from Modena.
Late goals from captain Mauro Icardi and Matias Vecino ensured Inter return to Europe for the first time since the 2011-2012 season, along with Juventus, Napoli and Roma.
Inter Milan chief has insisted striker Mauro Icardi is going nowhere despite his wife revealing two offers from big clubs.
Inter Milan defender Joao Miranda underwent clinical tests after suffering an injury to his left leg, the Italian club said.
Inter Milan ended a two-month winless streak in Serie A with a 2-1 win at home to nine-man Bologna on Sunday.
Luciano Spalletti's Inter leave Turin two points ahead of second-placed Napoli, who are level on 38 points with Juventus.
Icardi had been on form for Inter Milan scoring 11 goals in 12 games as his side are third in Serie A two points off leaders Napoli.