The 20-year-old Swiss international, who has been heavily linked with a move to Old Trafford, has branded his group stage opponents as having bad attitudes which resulted in their early exit.
Red Devils boss Sir Alex Ferguson is a known admirer of Shaqiri's, and was believed to be weighing up a bid for the attacking midfielder when the transfer window reopens in the summer. But, he is unlikely to warm to the player's recent comments about his team.
"United underestimated us. You could feel it in the tunnel and even in the warm-up," explained Shaqiri, who has since agreed a deal to join Bayern Munich.
"They weren't fully focused and I'm not sure a United player made one sprint. Afterwards, you couldn't even swap shirts - they were gone that quickly."
Basel have since taken a step towards the quarter-finals thanks to a 1-0 home victory over Shaqiri's future employers Bayern, in the first leg of their knockout tie, while Manchester United came through their last 32 second leg clash with Ajax last night.