Anderson headed home in first-half injury-time before Steven MacLean pounced with six minutes to go to seal a 2-0 win over Dundee United at Celtic Park and claim Saints' first Scottish Cup trophy in their 130-year history.
United twice hit the frame of the goal in an enthralling contest and Anderson said: "We deserved that at the end. We got a bit of luck to be fair and I think that's what you need in cup finals.
"We were in a decent run of form - I know we played well last week - but everybody was focused on the final. But, to be honest, I think we deserved it in the end and it's about time this club won something.
"It was a good year for a testimonial as well, but I'm just delighted for everyone at the club."
Striker Stevie May was booked for handball after punching the ball into the net, having thought his initial header had crossed the line.
"It was in already, I think," he said. "I thought it was already in and it just came back and I thought it had crossed the line before...it was more of a reaction than anything else."
"It's incredible, the group of boys here and what we've done this season has been outstanding.
"We've topped it off. We started unbelievably well this season and we've managed to do the same at the end as well."