The Toffees recorded an incredible 21st successive home league win against Fulham with a 4-1 victory to move into the top four ahead of Sunday's matches.
However, the performance was far from their best and, had it not been for a late rally with three goals in the final 17 minutes, the outcome could have been very different.
But Osman, who scored the opening goal on his 300th Premier League appearance, believes being able to win while misfiring as a unit bodes well.
"It was a bit sticky out there at times and not the most fluid we have played, but to come away with a 4-1 victory when you are not at your best is a good sign," he said.
"The team are very confident at the minute, we are playing well at times but we are not going to be able to be at our max every week. And when you can win when you are not at your best is great.
"At 1-0 we were just starting to find it difficult and their goal probably helped us more than it helped them."
Osman added on evertontv: "We have given ourselves a base, somewhere to go from and we can certainly turn this into a much better season.
"We have a lot of young players and a lot of experience and the characters in the squad are right.
"We have to aim high and see if we can reach it. We have our targets but we'll reveal them come the end of the season."
Everton have lost just once this campaign and are unbeaten at home in 2013, so when Osman gave them an 18th-minute lead with a well-constructed goal three points seemed a formality.
However, they could not turn their first-half dominance into further goals and the Cottagers found renewed energy after the break, leading to Gareth Barry bringing down Alex Kacaniklic in the penalty area to allow Dimitar Berbatov to score in successive matches.
Everton were wobbling but their nerves were settled six minutes later when Seamus Coleman scored his third league goal of the season, taking the tally scored by full-backs to seven in the campaign - equalling the club record from in 2001/02 - and there are still 22 matches remaining.
Barry atoned for his earlier error by nodding in from close range and Kevin Mirallas gave the scoreline a flattering look in added time with a shot which goalkeeper Maarten Stekelenburg should have dealt with better.
The only downside was a hamstring injury to on-loan Barcelona forward Gerard Deulofeu which will keep the youngster out for several weeks.
Manager Roberto Martinez praised the attitude of his players as they responded to the equaliser by bouncing back positively.
"The first half we played really well but if you don't get the second goal the opposing team will always have the opportunity. And the penalty, soft or not, was probably what we needed for us to start thinking we had something to lose," he said.
"We have been very good this season. Everything we try to do is brave, is attack-minded.
"I always measure a side by how you react towards adversity. We conceded a goal against Arsenal and reacted in the right manner (to draw 1-1 at the Emirates last week) and the same on Saturday.
"It would have been easy to feel sorry for ourselves. We were more focused than ever, we had a real threat."
Fulham head coach Rene Meulensteen believes his players have shown him enough in the three matches he has been in charge since Martin Jol's sacking to give him hope the second-bottom side can still survive.
The transfer window is still a couple of weeks away from re-opening and the Dutchman knows he needs to squeeze every last ounce out of the squad he currently has before then to give themselves the best possible chance of turning things around.
"That is the squad I am working with for the next few games and that is where I need to concentrate," he said.
"You need to keep a realistic view. In general there has been a positive trend (since he took over) with regards to energy, commitment and drive.
"There were some really good signs (against Everton).
"If we had been able to drag that one point over the finishing line it would have been a perfect follow up to the Spurs and Villa games (a 2-1 defeat and 2-0 victory respectively)."