"4 years is not enough.WTF!!! Oh well, it doesn't change what I do tomorrow!!! #drugcheat #belarusians," Adams tweeted.
Team Adams hoped for help from Athletics New Zealand to appeal against the length of the ban but Drug Free Sport NZ chief executive Graeme Steel said the chance had gone.
"Valerie is not in a position to appeal and the opportunity for anyone to appeal is over," Steel said. "The people who were entitled to appeal were aware of the decision and their opportunity to appeal."
Adams' manager, Nick Cowan, said they were only made aware of the ban yesterday morning and were disappointed the chance to appeal was gone.
"That comes as a surprise but I need to understand this better before I make a comment," he said.
"It's a good start but we were naturally disappointed because we expected it to be a heavier ban given it was two positive tests over a period of years."
The rules made it difficult for the IAAF to impose a lengthier ban. The ban for a second offence can be life but, given that Ostapchuk's 2005 offence was discovered as part of investigations into the 2010 one, it would have been difficult for them to regard it as a second offence.
"The four years would reflect an aggravated case rather than a second offence," Steel said.
New rules will be introduced next year that will see the standard ban for a drug cheat increase from two to four years. The onus would also be on the athlete to argue his or her case for a more lenient sanction as opposed to present rules which put the onus on anti-doping organisations appealing for harsher measures.
"Four years is substantially better than a one-year ban, which was the original proposal from the Belarus athletics federation.
"We see this person as someone who set out to cheat over a long period of time and they are the sort of people you want out of sport. It's good there is now a line in the sand and that someone who has cheated is out for a period. Whether it's long enough is a moot point but at least she's effectively out of the running for Rio."
Ostapchuk will be 36 in October 2016 and whether she has the ability and willingness to compete at the highest level again is unknown. Team Adams don't expect to see her in competition again but wanted that opportunity taken away.
"I don't expect to see her back but we had hoped the ban would have effectively ruled someone out of their career.
"She won't be able to compete at Rio because she won't be able to qualify for the Games ... but she could compete on the circuit in 2017 or 2018 and earn money."
Adams has recovered from knee and foot surgery last year, winning her 13th national title last weekend and 46th successive victory dating back to August 2010. She will next compete at a Diamond League meet in Doha early next month before this year's Commonwealth Games and Continental Cup.