Anderson retained his career-high 15th position after reaching the last 16 at the Australian Open in Melbourne last week. The tournament's 14th seed was knocked out by third seed Rafael Nadal, losing 5-7, 1-6, 4-6.
It was the third consecutive year Anderson had reached the last 16 in Melbourne, losing to Tomas Berdych on the two previous occasions.
Coincidentally, Nadal went on to lose against the Czech in the quarterfinals in Melbourne last week.
Klaasen, meanwhile, and his new partner Leander Paes of India, were knocked out in the second round of the Australian doubles event, by the unseeded Italian pairing of Simone Bolelli and Fabio Fognini. The 10th seeds won the first set but eventually lost the match 6-2, 4-6, 1-6.
Bolelli and Fognini went on to win the doubles, beating Pierre-Hughes Herbert and Nicolas Mahut of France 6-6, 6-4 in the final.
In the week leading up to grand slam event, Klaasen and Paes had won the Auckland Open.
Klaasen was runner-up in last year's Australian Open, partnered at the time by America's Eric Butorac.
Source: Sapa