The 2-0 win in a controversial Merseyside derby followed on from three points at home to Wolves last week and erased the memories of reverses at Stoke and, in particular, Tottenham.
"The two victories we've had back-to-back after the defeats has shown the character of the team and depth of the squad we've got here," said Downing.
"We all want to do well and getting wins like this helps.
"We played some good stuff at times but the sending-off killed them a bit and made it very hard for them.
"I wasn't near it at the time. It happened that quick I didn't have a great view of it but at the time I thought it would be a yellow card.
"It's easy for me to say that but it was a tough decision for the referee.
"But we kept pressing and it paid off in the end. Credit to the lads because we managed to exploit it in the end."