A brace from Harry Kane and further strikes from Christian Eriksen and Son Heung-min wrapped up the win at Wembley Stadium, and Allardyce was far from happy.
Everton failed to register a single shot on target and - following a strong start under Allardyce - they are now without a win from their last six matches.
Wayne Rooney thought he had opened the scoring for the Toffees only for his header to be correctly disallowed for offside. Allardyce felt Kane's opening goal could also have been ruled out.
"The disappointing thing for us is, what would the game have finished like had we scored the first goal when Wayne's got disallowed?" Allardyce said.
"Or what would the game have gone like if Harry's goal would have been disallowed - because I think it's offside looking on the laptop.
"What I can't excuse is out capitulation after we went 2-0 down. But for Jordan Pickford they would have had more goals today and I'm hugely disappointed in the professionalism of my players."