A double from James Rodriguez inspired the Colombians to a 2-0 win that saw Uruguay knocked out of the tournament.
"We knew that Colombia have individual players that contribute a lot to their team play," Tabarez told reporters.
"We have to accept the defeat and wish them that they do well as a fellow South American country. The only thought is that I'm very proud of the men that make up the national squad of Uruguay. They've given their all."
Colombia will face Brazil in the quarter-finals next Friday.