Although it came down to spot-kicks in the end, England could not argue as they had been second best while holding Italy in a goalless draw for 120 minutes.
Owen, a free agent after leaving Manchester United this summer, took to Twitter after the game to lament the absence of his former Old Trafford team-mate Scholes.
He wrote: "Pirlo was awesome but we have a player of a similar age and equally as good. Unfortunately he wasn't there. #Scholes.
"Easy for people to say 'until we keep possession better we will never win anything'. We are not as good as others at doing that.
"We played to our strengths but are just not quite good enough. We were hoping to 'do a Chelsea'. If you are not the best team then you have to find an alternative way to win. The other option is to forget results for a while and start from scratch playing a different style.
"Doubt we have the type of players to do that though. Answer has to be to start coaching our youngsters a different brand of football."
Another of Owen's former team-mates, Rio Ferdinand, sympathised with the England players but again pointed to Italy's midfield master Andrea Pirlo as the difference in the game, highlighting the Juventus midfielder's audacious chipped penalty in the shoot-out.
Ferdinand tweeted: "Wow, out on penalties again. Gutted for the lads man.
"On a pure footballing note Pirlo just put on a pure footballing master class + the penalty was too much".
The once-capped Joey Barton was, as usual, not short of an opinion either, saying England deserved to come in second best.
"What is it with us and penalties? Saved us from the embarrassment of a pasting off Germany in the next round" he wrote.
"Even the most biased Englishmen has to admit that Italy were much the better team over 120mins... #sadbuttrue".