Trailing 3-0 from the first leg at White Hart Lane, goals from Antonio Cassano, Rodrigo Palacio and a William Gallas own goal took the game into extra time, only for Emmanuel Adebayor to strike and see Spurs through 4-3 on aggregate.
“This is a fundamental sign we send out today and the only positive I can see from this evening is that we won’t have midweek games to worry about. It was our best performance of the season," he said.
“We have taken a huge step forward in terms of our play, we believed right from the first minute, we're still there, we've got ability, we're all together and we want to finish the season on a high. Tonight's performance was our best display in terms of the football we produced.
“The lads approached the match brilliantly, shrugging off any fear. It's just a shame about the result and the fact we conceded by switching off."
The Nerazzurri must now look to repair their stuttering Serie A campaign, with the club now sat in fifth spot following their defeat to Bologna last weekend.
But Stramaccioni remains buoyed by the spirit displayed by his men and their refusal to be broken by the criticism that has come their way in recent weeks.
He added: "You can't deny the fact that the Europa League takes its toll in the following game, especially after 120 breathless minutes here, but either way we've taken a big stride forward.
“Now we get back into league action. But at this time, with all the heavy and sometimes gratuitous criticism that we've come under, had we not been united, it would have torn us apart."