Celtic finished 16 points clear of runners-up Motherwell in the SPL but some pundits suggested Neil Lennon's men had stumbled across the finishing line.
Stokes, who scored the winning goal against Dundee United in the semi-final, said: "Have we had the credit we deserved this season? I don't know. When we were doing really well in Europe, everybody was talking about us being a great young side.
"But when you tail off with three or four games to go, people tend to have short memories.
"We will look back on it as a great season with a great run in Europe. We won the league fairly comfortably and our main aim now is to do the double.
"The league is the main aim year after year - it's the big one. I think we deserve the double this year.
"I wasn't involved in the Champions League run but I think the team has been outstanding throughout the whole season.
"I think we deserve to lift the cup based on the way we have been playing. Maybe I shouldn't say 'deserve' as we still have to go out and perform at the weekend.
"But I think the way we have played this season, it would put a bit of a dampener on things if we didn't go on to secure the double."
Stokes is out of contract this summer but has not given up hope of extending his stay in the East End of Glasgow.
"It's going on at the minute now and there are contracts getting sorted out. I'm confident enough it will be signed," he said.