The Italian giants were on the wrong end of a thumping victory for Andre Villas-Boas' side, and now have a mountain to climb in the return leg at San Siro.
And although the 37-year-old admitted Spurs were infinitely better than his outfit, he believes it could have been different had Ricardo Alvarez and Rodrigo Palacio not passed up gilt-edged opportunities.
He told reporters: “The real regret is we didn’t make the most of those two great scoring opportunities, as we could’ve kept the qualification a lot more open than it is now. We created the two cleanest scoring opportunities of the game.
“I think Tottenham were honestly superior tonight in different ways, but we suffered more than anything on a physical level. Two of the three goals came from situations where we paid for their height and strength in the air.
“We had tried to work on not allowing Tottenham to get enthusiastic by scoring early on, but it happened and made them even more aggressive. It was difficult to get service through to the forwards.
“We must play the second leg and try to win. Football is strange, so I think we can do well at home and try to score an early goal. Inter have already achieved special comebacks."
Inter had a host of injury concerns heading into the clash in north London with most noticeable absentees being Diego Milito, Walter Samuel and Yuto Nagatomo.
And Stramaccioni lamented that they were unable to field a full strength XI.
He added: “We have always showed that we believe and there are regrets we had to face this game with a line-up that was forced upon us and players who were not in great shape. Even then, we could’ve scored twice in London."
Tottenham took the lead through Gareth Bale as he rose above Esteban Cambiasso to header the hosts in front.
The Welshman will miss the second leg in Milan - where he rose to prominence back in 2010 - after picking up a booking, but Stramaccioni was full of praise for the 23-year-old.
He said: “I had already said Bale was one of the most decisive players in Europe and his header was worthy of a seasoned centre-forward.
"He can still improve a great deal, is very young and can be decisive, which is the difference between a good player and a champion.”