"I think at the highest level, like this, you have to expect to suffer like we did. PSV are a good team and it is a good result but we shouldn't be too self confident, the second leg won't be easy," said Ancelotti.
"We performed well in the first half but not in the second. After the break we were far too focused on defending and counter attacks. Luckily we managed to get a really great result out of the game," he added.
After Andriy Shevchenko had put Milan ahead, a last minute strike from Dane Jon Dahl Tomasson gave the Italian champions some breathing space for next week's return after PSV had gone close to an equaliser on several occasions.
"Playing against PSV is above all a question of rhythm. They don't have many dynamic players but when they brought the pace of the game down then they had us in some trouble," said Ancelotti.
"On the level of quality there is no doubt that Milan is a superior side but in these games experience counts a lot -- as does courage and personality. Their performance didn't merit a 2-0 defeat but we'll take it," said the Milan coach.
BEST FOOTBALL
Ancelotti was much more positive about the way his team put PSV under pressure in the first half, eventually taking the lead in the 42nd minute through Ukraine striker Shevchenko.
"In the first half we performed some of our best football of the season but at this point of the campaign we can't start celebrating yet," he said.
"We are under intense pressure and we have to think about Fiorentina on Saturday in Serie A," added Ancelotti, whose side are joint leaders in Italy along with his old club Juventus.
"We've baked the cake now we need to put the icing on it. We have to prepare well for the return leg and we need to weigh up how they caused us those problems in the second half."
Milan's Dutch midfielder Clarence Seedorf, who battled with PSV captain Mark van Bommel all night, admitted his side rode their luck at times.
"Without luck you don't get anywhere in this game," he said. "We created a lot of chances in the first half but they did well and then even better after the break. They showed they can play."
Substitute Tomasson's 90th minute goal could be vital but the Denmark forward, whose last gasp strike against Ajax in the quarter-finals two years ago helped Milan to a sixth Champions League triumph, was generous in his assessment of the game.
"PSV played an excellent game, both teams had a lot of opportunities, we didn't play as well as we could today but in general Italian teams have a problem against Dutch teams.
"You saw that against Ajax two years ago -- we beat them but we struggled," said Tomasson.
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