Sporting director Nick De Santis said Thursday that Klopas has done a good job preparing the club for games and that he still has the players' support.
The winless Impact (0-4-3), who were leading the league at this time last season, are last in MLS heading into a home game Saturday against the Philadelphia Union.
"The coaches, I can guarantee you, from the first day have done good work," said De Santis. "You can see the intensity from the players in every practice.
"Yes there's tension and pressure, less confidence, but that's pro sports. I think the team believes in the coach and will come out of this."
There has been speculation about Klopas' future among fans and media as the winless run to start the season — the worst in the team's 21-year history including its pre-MLS days — drags on.
It hit a fever pitch after last week's 4-0 loss at Kansas City.
If Klopas is feeling the pressure, he didn't show it.
"I know it's about results," he said. "I'm not here to make excuses.
"I'm very thankful to be part of this organization. I think Nick and all of us work hard. That's all I can do. I don't think about the other stuff. The only thing I can do is prepare the team and make sure we do as well as we can to get the team back on track."
The Impact will play their first game on the grass field at Saputo Stadium after three home games indoors at Olympic Stadium, where they had a loss and two draws.
Another defeat — in the first meeting between the clubs since Montreal sent Andrew Wenger to Philadelphia for Jack McInerney in a swap of strikers last month — would put more heat on Klopas, the former Chicago Fire boss who replaced the fired Marco Schallibaum in December.
There has also been criticism of De Santis, who made no major off-season moves despite a late-season tailspin and a one-sided loss to Houston in the first round of playoffs in 2013.
"I understand the frustration," said De Santis. "I'm from Montreal.
"I live here every day and I know how people feel. They have a right to criticize and I'm in a position where I have to accept that. But I'm very confident in this team and that, with a few additions, we can improve this team."
Since the start of training camp, the Impact have added former New York fullback Heath Pierce, little used forward Santiago Gonzalez, and made the McInerney trade.
De Santis said he is looking at adding a third designated player to go with striker Marco Di Vaio and midfielder Hernan Bernardello, and that he has his sights on Argentine midfielder Ignacio Piatti. He won't be able to sign anyone until the July transfer period, however.
In the meantime, the Impact have been pleading for patience.
Team president Joey Saputo wrote this week on Twitter: "Very frustrating start to the season. We need and will turn this around. Let's stay focused and determined. More than ever, we need our fans."
Despite their record, the Impact are only five points out of a playoff spot as the entire Eastern Conference has had trouble winning. Kansas City and Columbus share the conference lead with 11 points, including only three wins each in six games.
De Santis said that missing Di Vaio for the opening three games to a suspension and injuries to Bernardello and midfielder Sanna Nyassi have hurt.
He said the team has also been unlucky and could have won a game or two that slipped away.
Missing injured central defenders Nelson Rivas and Adrian Lopez has also been a problem as veteran Matteo Ferrari has found himself working with youngsters most weeks. Lopez, who blew out a knee after only one game for Montreal last summer, had his first full-field practice Thursday, but is not yet ready to play.
The oft-injured Rivas looked ready to return two weeks ago, but is back to running laps during practice.
Ferrari said he hasn't given up hope.
"I like the coach and the job he's doing because he's very professional," the former AS Roma and Everton defender said. "He likes the details and he prepares the game well.
"There's nothing I can say negative. If I look at the standings, it's bad, but the first place team has three wins, not five or six. So let's win a couple of games and then we'll be talking about something else."
Klopas also talked about Jeb Brovsky, a workhorse under Schallibaum last season who became a fan favourite for his toughness and his extensive work for charities and other causes. The third-year fullback has spent most of the season on the bench while Pearce played left fullback. Brovsky is likely to stay there for now.
"He played on the left side and I'm looking for more of a natural left-footed player," said Klopas. "On the right side, we have (Eric) Miller and (Hassoun) Camara, so there's competition.
"Jeb has handled it well. But to be fair, when you put him on the left side, it's not ideal, even if he played well last year. I'm looking for a left-footed guy that can open up the field, that can get crosses in. But he'll get opportunities."