The setback followed last month's Scottish Cup exit at Aberdeen, while a 1-0 defeat at St Johnstone on Saturday saw Hearts drop to sixth place in the SPL.
However, Zaliukas is determined to seal a top-six place and make the season a success.
"This performance was better," the Lithuania international said.
"We still have 10 games to go and we need to win as many as possible to be ready for the top six.
"I'm enjoying playing now and feeling confident and hopefully our results will be better and we can go to the top six."
Zaliukas believes only the end product was lacking for Hearts against Saints, who progressed thanks to Billy Mehmet's brilliant 25-yard strike.
"The final pass in the second half wasn't quite good enough," the 26-year-old told Hearts World.
"We almost had a couple of good chances but the final pass just wasn't good enough."
Jefferies also feels there is plenty to work with and is hopeful the team will quickly absorb his attacking principles.
The Hearts boss had Andrew Driver back in the starting line-up for the first time in three months and now has a spare weekend to put across his ideas.
"There's no need for the fans to panic about anything," Jefferies told Hearts News Today.
"The first thing we had to do was make sure that what happened at St Johnstone didn't happen again.
"Last night was a lot better in some respects but we know where we have to work on improving things.
"We will get in amongst them and we will sort it out but these things don't happen overnight and will take time."
Source: Team Talk