A sound defensive display helped Atletico earn a 1-0 first-leg advantage over Bayern Munich in the Champions League semi-finals on Wednesday.
Atletico, the 2014 Spanish champions, knocked out La Liga title rivals Barcelona in the last eight.
Allardyce said: "'He defends too much' - that's what he'd get here."
Bundesliga leaders Bayern dominated the second half after Saul Niguez's sublime solo goal had given the La Liga side an early lead, but Atletico's defence blunted their attack.
Allardyce, whose own methods have been labelled as dour in the past, added: "It's an art, defending - everybody has forgotten that. It's a tactical art to be able to sense danger and block people's crosses and get your toe in without fouling them now and they are very, very good at it indeed.
"The whole team buys into it. You see Fernando Torres on the edge of his own box defending. You never saw that at Liverpool or Chelsea.
"That's how good the manager is and that's why they are successful. They are successful because they concede fewer goals than everybody else and only need one to win.
"Now, everybody can say 'well, that's not entertaining', but everybody is eulogising Simeone's tactics now. I wouldn't think they would do that in the Premier League so much."
Atletico are only behind Barca in La Liga on head-to-head record with three games left.
Sunderland have collected three clean sheets in their last four games and the manager said extending that defensive record over the four remaining league matches was key to relegation survival.
The Black Cats - who moved out of the relegation zone last weekend but only on goal difference - play Stoke on Saturday.
"At the moment, if we keep those clean sheet ratios going in the next four games, I am convinced we will stay up," added the 61-year-old.
Atletico Madrid boss Diego Simeone would be labelled "boring" if he were managing in the Premier League, says Sunderland manager Sam Allardyce.