Both sides had already been relegated to League One, but Adkins insisted the Iron could hold their head up high this summer.
"This has been a terrific season for us and we have given it our best shot," he said.
"My players have shown commitment right the way through the campaign and they did it again when we were trailing 3-1 to Colchester.
"At the end of the day, we have come up just a little bit short of surviving at this level.
"But we won the League One title two seasons ago and promotion has got to be our aim as we look forward to next season.
"Like Colchester, we are a small club with small resources but there is no shortage of ambition to bounce straight back."
The Colchester manager Geraint Williams also has one eye on winning promotion next season.
"After two seasons in the Championship it really hurts to be going down. But this game just about summed up our season," he said.
"We scored three great goals and always looked dangerous going forward but after getting 3-1 in front, some poor defending once again let us down.
"We didn't want to be relegated with a whimper and I think we showed that. Now promotion has got to be the word as we look to next season in League One."