The Frenchman's career has been blighted by injury problems and, when his return to the France side after a four-year absence was curtailed by a calf injury in September, the thought crossed his mind that maybe it was time to call it a day.
Having decided to carry on, Saha battled back and was in prime goalscoring form when he damaged his ankle against Fulham in March, ruling him out for the rest of the season.
He said: "Sometimes you feel really unlucky and that it's not made for you but I've got full confidence in myself and my ability so, while I've still got the opportunity, I'm enjoying it.
"(Retiring) crossed my mind after my last cap with France when I had a really bad injury. It was really hard to take but now I've got older and I think I can cope more with this type of situation."
Saha has now returned to full fitness ahead of the new Premier League season and is hoping he will finally be able to show Everton fans what he is capable of over a sustained period.
He said of his troubles: "It's not nice but I'm happy to be playing again. I love the game so much. I love to see my kids be happy when I'm on the pitch and I feel privileged to be a footballer.
"Even if it's hard, you have to accept it.
"I want to be a better player, I want to score more goals, enjoy it more, get a better relationship with the fans and the club. I think I've got so many things to give to football again.
"In my head I feel more confident and more relaxed."
The summer has been another quiet one for Everton in the transfer window, causing anger among some fans about a perceived lack of investment in the playing squad, but Saha has urged them to have faith in the club.
The 33-year-old said: "It's not the right way to start a season but I'm here to kick the ball and make sure we're winning games. I understand their concern but they have to be confident in the team and the squad.
"They should know the chairman and the board and the manager are trying hard.
"They're desperate to do something but if they're not doing something it's because they've got big reasons for that. You have to trust them. We trust them as players."
Everton are scheduled to begin the season on Saturday with a trip to Tottenham, although that could yet be postponed because of the trouble that has flared on London's streets.
Whether they begin against Spurs or the following week at home to QPR, the Toffees will hope they can avoid another poor start.
The last two seasons have seen David Moyes' team struggle over the first couple of months.
Saha revealed they have been working hard to prevent a repeat and, despite a lack of new signings, the Frenchman believes Everton should be looking to challenge the likes of Tottenham for the European places.
He said: "We've changed quite a few things around the training and the tactics.
"Maybe the mentality was not right. We've trained hard to solve the problems. Everybody is confident we're going to do something special this season.
"We've got so many players who are good enough to show that we can break the top five this year. We didn't start well last season so that's the aim."