Simone Inzaghi was full of praise for his Inter Milan side after a 2-0 win against rivals AC Milan in the away first leg of their Champions League semifinal but said they should have scored more than two goals in an "extraordinary" first half.

Edin Dzeko gave Inter the lead with a fine volley after eight minutes at the San Siro before Henrikh Mkhitaryan doubled their lead just three minutes later.

- Olley: Inter steal the show as raucous San Siro takes centre stage
- Stream on ESPN+: LaLiga, Bundesliga, more (U.S.)

But with Hakan Calhanoglu also hitting the post and Inter having a penalty award overturned following a review of a challenge on Lautaro Martinez, Inzaghi said they should have made more of their early dominance.

"We had an extraordinary first half, the scoreline was tighter than it should have been, with what we created," Inzaghi said. "The guys were really great in managing such an emotional match.

"We have to continue like this. We know that we're just one step away from a dream that we believed in from August until today."

The second leg is on Tuesday, in what will surely be another special European night at San Siro when Inter will have the benefit of home support at the stadium they share with their city rivals. The winner will face either Real Madrid or Manchester City, who drew their first leg 1-1.

"This is obviously a derby, so it's even more emotional," Inzaghi added. "The lads know that we have to do exactly what we did against Benfica [in the quarterfinal]: not thinking about managing the match, but playing our own game, with the quality that we have shown on the field."

Milan were missing key forward Rafael Leão, who hadn't fully recovered from a thigh injury sustained over the weekend, and defender Fikayo Tomori admitted that they initially failed to deal with the pressure of a semifinal that had been dubbed the "Euroderby" in Italy.

"Obviously disappointed. Just the way we started the game, conceding two early goals like that," he told BT Sport. "The first one from a corner and then straight after. It's difficult when it's 0-0 but to go two goals down in the first 15 minutes is a kick in the teeth.

"It took us a while to get back in the game. There was a bit of anxiety in the team. In a game like this you can't do that."

Milan improved in the second half and were shooting toward the end packed with its fans, in a sea of red and black.

Brahim Díaz curled wide of the left post early on but Inter were almost out of sight moments later. No one closed down Alessandro Bastoni and he threaded the ball through to Dzeko but goalkeeper Mike Maignan somehow managed to parry the shot with his foot.

The Rossoneri should have pulled one back in the 63rd minute but Sandro Tonali's effort came off the base of the left post.

"I know my team, I know my players, I know we can do better," Milan manager Stefano Pioli said. "I know Inter is a very strong team, but we're not any less. It will be a difficult night mentally for both teams, the last chance to get into the final.

"We have the chance to put them in difficulty, to score goals, to try to get this back on track ... We have to give everything we have -- talent and heart -- to turn around a situation that has become difficult but not impossible."

Information from the Associated Press was used in this report.