Sir Terry said: "As the UK's leading supermarket we thrive on competition.
"We have a strong strategy for growth in food, non-food, retail services and overseas which we look forward to continuing."
Asda chief executive Tony DeNunzio said:"Naturally we're disappointed with this decision.
He added: "We will press on with our plans to grow the business and expand our store network and I know the 124,000 great colleagues who work at Asda are geared up to deliver a fantastic Christmas for our customers."
Sainsbury also said it was disappointed to have been blocked from bidding for Safeway.
But group chief executive Sir Peter Davis said he was encouraged that it had the chance to bid for some of the stores that Morrisons must sell and believed Sainsbury was "well placed to bid for a worthwhile number of these stores".