The veteran midfielder's goal in the 80th minute gave the Impact a 1-1 MLS draw with lowly Chivas USA on Sunday night.
The Impact (9-4-4) lead the Eastern Conference with 31 points, but are 0-1-2 in their last three games, including a 4-3 loss to Colorado in their previous home game last week.
"It's not our greatest period, but these things happen," said Bernier. "We have to refocus, regroup, and find some energy.
"We have some tough games coming up and that will be a good challenge."
Eric Avila, recently returned from a trial with Mexican club Guadalajara, scored for Chivas (3-10-4), the last-place team in the Western Conference. Chivas has gone 13 games without a win dating to a 2-1 victory over Vancouver on March 30.
On paper, they were easy pickings for Montreal's high-powered attack, which leads the league despite having played fewer games than most MLS clubs.
But on the field, Chivas played a thorough and patient defensive game while the Impact wasted several good chances.
"It's nice to come back and get a point," added Bernier. "In the end these little points will count.
"But we wasted enough chances that we could have had a two-goal lead. But that's football."
Chivas opened a three-game road trip with a 0-0 draw in Dallas and will be looking to add more points when they visit Toronto FC on Wednesday night.
Goalkeeper Dan Kennedy, who stopped Marco Di Vaio and Felipe Martins on early point-blank chances, sees his team getting stronger under new coach Jose Luis Real.
"We knew this would be a tough game and we came prepared and we put in a smart performance," said Kennedy. "We didn't leave ourselves too vulnerable.
"We stayed compact and limited their chances. It was a great point for us."
Bernier used his signature stutter-step move to score from the spot after Mario De Luna took down Sanna Nyassi on the left edge of the penalty area.
The Impact have struggled on defence, allowing eight goals in their last three outings, and it surfaced once again as low-scoring Chivas got the first goal in the 55th minute.
After Hassoun Camara lost the ball near the halfway line, a Jose Correa cross into the middle looked to put Montreal in panic mode. Jorge Villafana blasted a left-footed shot off the bar and Avila was there to put in the rebound from the edge of the penalty area.
It was the one setback in an otherwise better defensive performance than their last two outings.
And it was their second comeback draw in a row after tying 3-3 in Toronto during the week.
Coach Marco Schallibaum called it a good effort and added "the balance was better today.
"There are no easy games in this league. We had a lot of good chances but the goalie made some god saves. We are also missing some of the lucky punch we had before. But we went for the win at the end."
Montreal outshot Chivas 18-8, including 8-3 in shots on goal.
Substitute Andrew Wenger had two good chances in the dying minutes, but put one shot just wide and the other was stopped by Kennedy.
Chivas defender Carlos Borja took a yellow card but saved an almost certain goal when he pulled Di Vaio down from behind just outside the area in the 39th minute.
Montreal reached the halfway mark of their season. After 17 games as an expansion team in 2012, they were 5-9-3 for 18 points.
Notes: The Impact brought Davy Arnaud and Bernier out of the starting 11 in favour of Nyassi and Collen Warner. Warner played his 50th career MLS game, while Bernier went on in the 68th minute for a team-leading 33rd straight appearance. . . Matteo Ferrari wore the captain's armband. . . Schallibaum was back after serving his third one-game suspension Wednesday in Toronto.. . Tristan Bowen (suspension) and Julio Morales (national team duty) returned for Chivas but didn't start. . . Chivas beat Montreal 2-1 in their only meeting last year in Carson, Calif.