First-half goals from Andriy Yarmolenko and Roman Yaremchuk gave Ukraine a Group C win in Bucharest.
Ruslan Malinovsky missed a late penalty to make Ukraine sweat after Ezgjan Alioski pulled a goal back, following up when Georgi Bushchan saved his spot-kick.
Shevchenko said: “This part of the European Championship is a very different atmosphere, during any second the balance of the team can change. The team played a very good first half but then our mistake caused a penalty.
“Then some anxiety and nervousness appeared. We got more chances and should have scored a third but we also have to praise our rivals. North Macedonia have character.
“We had enough chances to score more, to judge how we score and when you need to see how many chances we have, how we played in attack and what opportunities we have.”
Ukraine delivered two quickfire blows in the first half when Yarmolenko and Yaremchuk struck inside five minutes.
West Ham’s Yarmolenko opened the scoring after 29 minutes when he converted from close range after Oleksandr Karavayev flicked on a corner.
Yarmolenko then turned provider when he slipped in Yaremchuk to beat Stole Dimitrievski low to his left.
Goran Pandev had a goal disallowed for offside soon after but North Macedonia did pull a goal back after 57 minutes.
Karavayev brought down Pandev after Bushchan brilliantly turned Aleksandar Trajkovski’s shot on to the bar. The goalkeeper saved Alioski’s penalty but the Leeds man followed up to score.
Ukraine had chances to avoid any late nerves and Malinovsky saw his penalty saved by Dimitrievski with six minutes left after Daniel Avramovski handled the striker’s free kick.
North Macedonia boss Igor Angelovski said: “The match is 90 minutes and the goal was to be more cautious in the beginning, unfortunately we conceded from a corner.
“In the second half we saw the real Macedonia and why we are here at the European Championship. Congratulations to the boys for the great game in the second half. If the public reward you with that kind of applause it indicates you have played a good match.
“You saw, unlike the first game, they played completely relaxed and that was the real Macedonia. There is no greater motivation than to play against a big Holland team (next).”